I am not very familiar with these styles, but I think the key differences are these: House is the most mainstream of the three. It features shorter, simpler songs which are similar to "Schlager" or MOR songs, albeit mostly with a stomping rhythm. (good with alcohol) Techno is concentrated on electronic beats and has very long pieces to be danced to ecstatically. Trance developed out of techno or is related, but there is more emphasis on floating sounds and a chillout or meditative atmosphere. Maybe some expert will correct me with that, but that is the way I would define the three.

Arguably it's the beats per minute. House<130bpm, Trance 130-160bpm with ethereal noises, Techno 160-180+ bpm hardcore usually with a chill out middle 8. Check out the Ministry of Sound webs site. http://www.ministryofsound.com/

sorry jo kool but you're wrong. techno has completely changed - it was once 160-180bpm but now it has slowed down to the pace of house music, it has become a lot more melodic and can be very gentle. the key differences are - house is classic 4/4 structure, after every 16 bars something drastic happens to the song. with techno the beat can just seem to flow with only a hi-hat being added after 16 bars. make sense? it's hard to explain. techno just plods and the songs build very subtley, whereas house you know exactly when its going to build up / drop. (new) techno is what is being played in all underground clubs at the moment. Trance...!? wasn't that some ancient music form of our ancestors? (jo-kool was right about that - usually 150bpm)

matt_fireflytv is right about techno in his first paragraph. But trance is usually 130-140 bpm. As for differences besides tempo: I would say house focuses more on melody and has a more prominent bassline. It tends to be upbeat and provocative and makes you want to move your hips. It feels warmer and often uses more live-sounding samples. Most house is influenced at least somewhat by funk. You could compare house music to a funk band. Trance focuses more on chord progression and layered sounds. Even when played at the same tempo as house it tends to have faster rhythms. So it's busier both sonically and rhythmically. Another big thing is the build-up, breakdown, drop structure. House builds and releases energy, but not to the epic extent that trance tends to. Trance will often have long breaks where there is no beat and the tension just keeps building until the beat drops back in. Trance can be uplifting but it tends to have a more dramatic and sometimes dark mood. It can feel colder or more completely electronic than most house. You could compare trance to an orchestra in some ways. Techno today is more about unique sounds and rhythms. It tends to be darker and colder like trance, but even more minimal than house. Energy changes are more subtle. It sounds the most mechanical of the three. Then you have things like progressive house that provide a gray area and all kinds of sub- and hybrid genres that make everything hard to categorize. Progressive house takes a lot of elements of trance and techno, enough that it doesn't always feel like house, but retains enough house characteristics that it can still be considered house. It sits happily (though ambiguously) between house and trance in most contexts.