Bought new chain. Do I have to remove links? I have this bike I got it from wal-mart many years ago. Same as this one on amazon:  Denali 

The chain rusted. I noticed that it listed the chain on amazon. Chain: KMC Z 51
I bought this one.  

I'm trying to put it on and figure out how it goes through the derailleur I think I figured it out. But it seems too big. Maybe I just didn't put it on right. 

Do I need to resize the chain to fit my bike? Are they standard sizes?
Chains normally come with more links than you need, and you should use a chain tool to remove the excess links from the chain prior to installing it. 

This link from park tool shows you how to size a chain (but the easiest way is normally to just match the length to your old chain provided it was adequately sized and you didn't change anything else). This link will show you how to install a chain.