can I trade randomly in game or do I have to find someone to trade with? I really don't want to have to buy a second ds and white 2 just to get the last 5 Pokemon for my pokedex.
In your case, no. Unfortunately the only way for you to get the Pokemon you want without a second DS would be to trade over the internet. However, now that Gen 5 games are considered outdated, it is no longer possible to make trades over the internet with those games.