You are going to get all the smart arses coming on saying that Chinese bikes are crap and you should not have bought one etc etc. Well don't pay attention to them, it is easy to be smug over the internet.
In simple terms an engine needs the following to work: spark, compression, fuel/air mix. These are all basically easy enough to figure out.
1) Spark -remove the plug from the head, connect the HT lead to it, hold the other end so it is touching the engine itself and then kick the bike or turn the electric start. There should be a nice spark jumping across the gap at the end touching the engine. (Make sure the end of the plug is always in contact).
2) Fuel/Air Mix: Put the spark plug in and attempt to start the engine a few times. Assuming that it does not fire up then whip the plug out again and take a look at it. You should see it visibly wet if fuel is getting through.
3) Compression : If you have a kick start in the bike then you should be able to feel the engine being a bit harder to turn over on the kick start as you slowly swing it through it's range of movements as it hits the compression stroke. If it is easy to push the kick start with your hand all through the range of motion then your compression has gone west. If there is no kivk start or you want to try another method then take the spark plug out of the engine and press your thumb over the hole it was in to make a seal. Now turn the bike over as if you were trying to start it, you shoul dfel the pressure build up beneath your thumb and actually it will force your thumb out of the way. (Not painful).
So try those things first.
1. If no spark - try a different plug, see if problem goes away. If new plug still shows no spark then check that your engine cut out switch is not faulty and is cutting the ignition. If that is OK then there are other things to check that would be better done face to face with a technician.
2 - No fuel. Check that your fuel tap is not faulty. Take it out of the tank and ensure that fuel can pass through it no problem. Check that the fuel pipe is not pinched between the tank and the carb. If all OK and you feel confident then take of the carb and very carefully take of the bottom bowl part of it and see if there is any crap sitting in the bottom. If there is then there is a good chance that the jets are blocked. They will need clearing out with an air line - don't be tempted to stick a bit of wire in them. If you can't get any further or are not confident with the carb (which is a precision piece) then call a tech.
3 - no compression. This is the worst carse scenario and you will need to strip the top of the engine to find out what has happened.
In 90% of cases it is something simple and in spite of what people say the Chinese engines will last well enough if you take care of them.
Is it a two stroke or four stroke by the way?