There are a very large variety of mosses available that grow well in aquariums. The most common species available is probably Java Moss (Taxiphyllum barbieri). Other common mosses in the aquarium trade include:
Christmas Moss (Vesicularia montagnei)
Anchor Moss (Vesicularia sp Anchor moss)
Weeping Moss (Vesicularia ferriei)
Flame Moss (Taxiphyllum sp Flame moss)
Taiwan Moss (Taxiphyllum alternans)
Often included in this discussion are Riccardia chamedryfolia & Riccardia graeffei which are actually liverworts rather than mosses, but they tend to be grouped together with the mosses as they have similar utility and growth requirements. There are many other moss species of interest to collectors, but may not appear regularly in commercial trade.
All moss species handle similarly though they can have different growth forms. There are a few aspects of mosses that make them very different from regular aquarium plants.
Firstly, they are very hardy and have lower demands for light, Co2 and nutrients compared to other more demanding aquarium plants. Mosses (virtually all species) are almost indestructible in most tanks as long as the tank has clean, filtered water and stable parameters. Unstable parameters and poor water quality can melt mosses or lead to slow deterioration over time.
Mosses in general do prefer lower temperatures, and may not do well in warm tropical tanks where the temperature rises above 28 degrees celsius. They are best keep in cooler tanks below 26 degrees celsius. In higher temperatures, most species can still grow, but their form will not be as tight and coloration may be a tinge yellowish rather than green.
Mosses are also vulnerable to algae - and this is the principle reason why many planted tanks fail at keeping nice moss. While mosses themselves have very low requirements to grow and survive, keeping the tank algae free to display them nicely is a whole other challenge. This aspect is what limits its usage in the aquarium hobby, even though most mosses can grow in most tanks as they can survive in an extremely large range of parameters with low demands on light, CO2 or nutrients.
Java moss is by far the most hardy type of moss, it can grow in much warmer temperatures and tolerate poorer water quality.
The slower growing liverwort Riccardia is probably the more picky species on this list. To grow it to good form, it does best with CO2 injection, cooler water, and regular nutrient dosing.
All aquatic mosses attach to hard surfaces naturally over time, and do not require any substrate to grow. Big bunches of moss could be grown straight on the tank substrate, however, the most common way to use moss is using it to 'paint' surfaces of rock and wood. This allows moss to take on the contours of the hardscape and give a naturalistic aged feel to the rock and wood. As moss prefers a stable environment to propagate, attaching them to hardscape where they can sit permanently is ideal.
Moss can be propagated from the tiniest fragments. Larger strands of moss can be chopped up into smaller pieces (0.5 to 1cm) and these smaller strands will grow out. To get an even coating when attaching to hardscape, longer strands can be broken apart to smaller pieces before attaching.
There are a few methods of attaching moss to hardscape. One conventional method is by tying using fishing line or cotton thread. Thread is easily to handle for most hobbyists. Large moss pieces are broken down/chopped into easier to handle lengths (about 1-2cm), then wrapped onto wood/rock surface with thread.
A newer method of attaching mosses is by using super glue. This method requires a bit more practice, but gives more precision to planting specific small areas. It is also much faster. Using gel type super glue (check to make sure its made of ethyl cyanoacrylate), add a drop onto a finger tip size sample of moss - then press the moss against wood or rock and hold for 15 seconds before releasing. Super glue does leave white glue marks on hardscape, but these marks will be covered by moss in time. They can also be scrapped off manually.
Mosses can be propagated from very small fragments. You can trim moss down like giving someone a haircut. The spare pieces can be re-attached elsewhere and they will regrow into new patches of moss. This is both a pro and a con. The advantage is that moss is really easy to propagate. The downside is that all the small bits and pieces that you do not manage to capture when you do trimming work will spawn moss patches everywhere in the tank where they land - as long as they get access to light. This can smother slower growing species such as Bucephalandra.
While trimming moss, you can use a siphon with a net at the end to capture the moss bits.
Mosses are quite vulnerable to algae infestation. Due to moss's fine texture, it can be difficult to separate the algae manually. Mosses can also be sensitive to algicides. The best method is to trim off the surface of the moss layer that is infested with algae, and allow the bottom portion to regrow. However, this only works if the moss has favourable conditions to regrow - one must also take care to prevent algae from spawning continually, if not the problem will persist.
Having conditions that allow moss to grow robustly and out-compete algae is still the best way to have algae-free moss. This is where CO2 injected tanks have a tremendous advantage, as mosses will grow faster and more robust when CO2 is readily available. In such conditions, moss grows rapidly, and removing algae infested growth - allowing clean portions to regrow is an easy solution.
Mosses are ideal decorations for smaller size tanks. In this top view of a 9 gallon tank, many different mosses are glued onto wood to give a range of different textures. Front view of the tank is below:
In this 9 gallon tank, moss is used to fill out the foreground and hide connecting seams between the rocks and wood.
Moss used give a naturalistic and aged texture to hardscape.