二 is a pure counting numeral, so we use it like "一二三..." "一點，二點，三點。。。" So like "one two three...""one'o'clock, two'o'clock" and so on.

兩 is used when there are two things being counted; it's a lot like saying "a pair of".  So use it when you're counting something with a noun attached to it. "一碗湯`，兩碗湯。。。” “請給我兩塊”　These translate into "one bowl of soup...two bowls of soup..." and "Please give me two kuai (Chinese dollars)".

If you're looking for the 'Number 2 Train' you are probably looking for the "二號的火車”.  See?  It's not counting, it's just a numeral here.

It's actually pretty straightforward, and shouldn't be that much of a headache trying to figure out which one to use （ever try counting in Korean?  It's a nightmare).