I play with humans and make contakt to other races as fast as possible.

In MOO2:

Go to races, then audience, then select the race to make contact with.

IF the race or you are repulsive, your diplomacy choices are limited.

Also, quite often alien races have a neutral opinion of you when you first meet them. You can tell how they feel about you by looking at the vertical indicator bar next to their picture on the 'Races' screen (low/red = hostile, middle/yellow = neutral, high/green = friendly).

If you do nothing when you first meet an alien race, each turn the relation indicator bar will decay a little till eventually the aliens turn hostile and (very likely) declare war. To counter this, on the first turn of contact you should try and gain an audience with their ruler and do one of the following:
1. Propose signing either a trade or research treaty. This is usually only successful if the relations bar is slightly positive/green or your score in the score graphs is very strong. Each race has a natural preference for either trade (ie. Gnolems) or research (ie. Psilons) and will be more likely to respond positively to such a treaty. Once you have established a treaty, each turn your relations improve slightly with that race rather than decay.
2. Offer a gift. Once again certain races prefer money while others prefer tech or even an entire star system. This usually bumps up your race relations slightly, and now you can try to sign a treaty again with a better chance of success.
3. Exchange tech. Similar to offering a gift, this will slightly improve your relations and might be enough that you can successfully ask for signing a trade or research treaty. Beware exchanging tech with a race that might then give it to your enemies to use against you!
4. If they perceive your race as weak (likely due to your standing in the score graphs), they might refuse to sign any treaty at all. In this case, offer tribute. When you pay tribute, each turn your race relations improve by a small amount rather than decay. Sometimes you can get away with only paying 5% tribute, but most times you will need to pay 10% tribute. After 5-10 turns you should see enough improvement in the relations bar that the aliens will agree to sign a trade or research treaty.

Once you have established a treaty with an alien race, wait enough turns for the alien to contact you and thank you for signing the treaty. By then, your relations should have improved enough that you can ask for an audience and the aliens will agree to sign the remaining trade/research treaty type as well. Now wait some more turns till your relations improve even further (usually the bar needs to be 3/4 full/green or more) and ask for a Non-Agression Pact.

Once you have a NAP, you can consider cancelling any tribute. Your relations will drop quite a bit once you cancel tribute (and this can be dangerous if you are perceived as very weak), but they should steadily improve again thereafter as long as the trade/research/NAP treaties are in effect.

While you can't sign treaties with Repulsive races, you CAN spy on them without worrying about them declaring war. In any case, even with any hostile race that is still at peace with your empire, if you don't trespass into their star systems and have a strong enough fleet in the score graphs, they might leave you alone without declaring war even while maintaining a very hostile diplomacy rating (this is not likely, but it can happen).