Bio-hydrogen is hydrogen produced biologically by any of several processes: 

1)Splitting water using light by photosyntheses

     a) as a byproduct of making carbohydrates

     b) as a byproduct of making protein - nitrogen fixing

2) Extracting H₂ from organic compounds:

     a) dark fermentation - without using light

     b) photofermentation using light for energy

     c) electrochemically via microbial electrolysis

     d) thermochemically via pyrolysis and gasification

Photosynthesis

In photosynthesis, a plant splits water to produce hydrogen in two different ways for two different purposes:

1. so it can combine H₂ with CO₂ to produce carbohydrates.
2. So it can combine H₂ with nitrogen to form ammonia and then proteins.

Hydrogenase

The process of producing carbohydrate uses the enzyme hydrogenase.

Hydrogenase is a biological catalyst. A catalyst is like a hole in a dam wall allowing water to flow downhill without having to first find the energy to rise up over the wall.

A catalyst allows a chemical reaction to occur without having to supply the activation energy, or high temperature, to start the reaction. In this case it allows the energy from light, or oxidation of carbon, to split water.

To generate H₂, green algae and cyanobacteria employ different types of  hydrogenases: [FeFe], [NiFe], and metal free enzymes.

Hydrogenase occurs in both photosynthetic and non-photosynthetic microbes.

Oxygen prevents the hyrogenase enzyme from performing, and a lot of research work is going into ways of keeping oxygen separate.

Hydrogenase ezyme

Nitrogenase

To make protein, plants fix nitrogen. In this process they split water to produce hydrogen and then combine it with N₂ for the production of ammonia NH₄. This is the first step in making protein.

In this case the enzyme is Nitrogenase. If there is not any nitrogen present then the hydrogen produced can be harvested.

Both enzymes are metalloproteins containing iron-sulphur [Fe/S] clusters, while nitogenase enzymes also contain molybdenum-iron [MoFe] clusters. Sometimes the Mo is replaced with Vanadium.

Nitrogenase: Producing H₂ while fixing nitrogen

Cyanothece 51142 was discovered in 1993, off the coast of Texas, by Louis Sherman of Purdue University in West Lafayette, Indiana. Pakrasi later discovered that the bacterium has a two-stage daily cycle. During the day it undergoes photosynthesis, using sunlight and carbon dioxide to make oxygen and branching chains of glucose molecules called glycogen. When the sun goes down, the microbe's nitrogenase enzyme kicks into action, using the energy stored in the glycogen to fix nitrogen from the air into ammonia. Hydrogen is formed as a by-product.

The two mechanisms are different in that photosynthesis is an aerobic process — one that requires oxygen — whereas nitrogen fixation, and, consequently, hydrogen production, can take place only anaerobically, because contact with oxygen destroys the nitrogenase enzyme. But Cyanothece 51142 manages to fix nitrogen even in the presence of atmospheric oxygen by burning cellular oxygen to produce energy. Because no photosynthesis is taking place, the bacterium uses up its cellular oxygen so that the nitrogenase enzyme is effectively in a largely oxygen-free environment. Source

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The cyanobacterium Cyanothece 51142 produces hydrogen in air.  Pakrasi Lab

Hydrogenase: H₂ from making carbohydrates -algae and cyanobacteria

This process has the potential to convert sunlight to fuel about 100 times as efficiently as corn to ethanol.  (Admittedly a very low starting point. - Ed.)

Algae normally use photosynthesis to split water and combine the hydrogen with CO₂ to produce carbohydrates. Oxygen is given off as a waste product.  In 2000 it was discovered that If the algae C. reinhardtii are deprived of sulfur, they will switch from the production of oxygen, to the production of hydrogen.

The algae do this by producing and using an enzyme as a biological catalyst, and the energy in light. The enzyme is called hydrogenase.

In many industrial processes microorganisms are used to produce enzymes, then the enzyme is removed and used alone as a catalyst. If this could be done for hydrogenase, then all you would need would be the enzyme, water, and sunlight. However hydrogenase is not robust enough to survive by itself, so a lot of work is being done to improve or re-engineer it. 

Scientists at the U.S. Department of Energy’s Argonne National Laboratory are currently trying to find a way to introduce hydrogenase into the photosynthesis process. The result would be a large amount of hydrogen gas, possibly on par with the amount of oxygen created. Wikipedia

Recent history

2006 - Researchers from the University of Bielefeld and the University of Queensland genetically changed the single-cell green alga Chlamydomonas reinhardtii in such a way that it produces an especially large amount of hydrogen.
2007 - It was discovered that if copper is added to block oxygen generation algae will switch from the production of oxygen to hydrogen
2008 - Anastasios Melis  achieved 25% efficiency out of a theoretical maximum of 30% energy conversion efficiency in mutants of Chlamydomonas reinhardtii.
2011 - A  bioengineered enzyme increases the rate of algal hydrogen production by about 400 percent.
2011 - A team at Argonne's Photosynthesis Group demonstrated how platinum nanoparticles can be linked to key proteins in algae to produce hydrogen fuel five times more efficiently.

Source: http://en.wikipedia.org/wiki/Biological_hydrogen_production_(Algae)

Biopotolysis - hydrogen production from algae using light and water only.

Dark fermentation

Dark fermentation decomposes organic molecules such as sugars to produce hydrogen and volatile fatty acids VFAs. The process uses the energy stored in organic compounds. It is a good way of producing H₂ from food and other organic waste.

it is possible that under nitrogen limitation, some Clostridiaspecies should be able to produce hydrogen via nitrogenase with high rates. Dark anaerobic CO decomposition to H2 and CO2  by bacteria from different groups (including some purple bacteria) is potentially valuable process,which might be applicable for syngas purification with simultaneous production of H₂ and other useful products.

This highest rate by 2012 is 15 L H₂ per L of reactor per hour.

There is a big advantage in using high temperature fermentation. At 25^oC the reaction is endothermic (takes in energy) but at 70^oC, it is exothermic.

Dark fermentation is not yet very efficient and needs a lot of work before it is producing economic yields of H₂.

Photofermentation​

Photofermentative hydrogen production is a bioprocess in which photosynthetic purple non-sulfur bacteria (PNS) grow on organic acids like acetic, lactic and butyric acid (volatile fatty acids - VFA) and produce hydrogen using light energy under anaerobic conditions.

The VFA come from dark fermentation.

Integrating dark and photo-fermentation

Theoretically,each mole of glucose could produce 8 mole of H₂ from sugar, starch or cellulose.

  C₆H₁₂O₆+ 4 H₂O   ---->  8H₂  +  4CO₂ 

Technical University of Vienna describe their process below:

University of Birmingham are working on a very similar process to produce hydrogen from sugar from food waste and sunlight. They call their process An "Integrated Biohydrogen Refinery (IBHR)"

Bio-hydrogen production from sugar and sunlight

1. Convert waste food (sugar and starch) to sugars by mixing with hot water (200-260 °C) under pressure. This process is called "hydrolysis". 
2. Electro fermentation  - Dark fermentation using E.Coli. converts the sugars to hydrogen and volatile fatty acids VFA. The "electro" part of the fermentation is to separate  ammonia NH₄ from the VFA.  NH₄ inhibits the next fermentation.
3. Photofermentation using purple bacteria (Rhodobacter sphaeroides) to convert volatile fatty acids to hydrogen. Oxygen kills this reaction so must be removed as it forms.

Using more of the sunlight spectrum

Purple bacteria uses mostly Infra Red to grow and produce hydrogen H₂.

Green algae used to produce H₂ or other biofuels, use visible light.

They cannot be grown together as the oxygen produced by the green algae prevents purple bacteria producing H₂.

So the light could be split into visible and IR with a dichroic mirror. Together, the two beams have 171% of the energy of the visible light.

The practical details for this to work could be an interesting design exercise.

E. Coli

Escherichia coli is capable of producing hydrogen under anaerobic growth conditions. Formate is converted to hydrogen in the fermenting cell by the formate hydrogenlyase enzyme system.  Source

BioHydrogen production via electrohydrogenesis

hydrogen production is possible from any type of biodegradable organic matter by electrohydrogenesis. In this process, protons and electrons released by exoelectrogenic bacteria in specially designed reactors (based on modifying microbial fuel cells) are catalyzed to form hydrogen gas through the addition of a small voltage to the circuit. Hydrogen gas was produced at yields of 2.01–3.95 mol/mol (50–99% of the theoretical maximum) at applied voltages of 0.2 to 0.8 V using acetic acid. Ref NSF

Yields of 91 percent using vinegar (acetic acid) and 68 percent using cellulose

Even with the small amount of electricity applied, the hydrogen ultimately provides more energy as a fuel than the electricity needed to drive the reactor. Incorporating all energy inputs and outputs, the overall efficiency of the vinegar-fueled system is better than 80 percent, far better than the efficiency for generation of the leading alternative fuel, ethanol.

NSF 2007

In a microbial electrolysis cell, bacteria break up fermented plant waste to form hydrogen

Ref:

http://books.google.com.au/books?id=6o0brBy3sEkC&dq=hydrogen+produced+during+nitrogen+fixing&source=gbs_navlinks_s