How do you ensure security?

I realise this is a rather broad question, and a very noobish one, so bear with me.

Essentially what should I be aware of, and how do I know when I'm compromised?

Is it possible for something to hook into another process without me knowing? I feel like it is (eg browser) and that's worrying.

How are repositories kept safe? Are packages susceptible to interception? Can I verify packages?

I'm sure you can tell I have virtually no knowledge in this area, just enough to be worried :P.

Oh and I'm planning on going through and cleaning up a few packages that I won't need, just for neatness really. I'm pretty sure it's not possible but I can't accidentally open myself up to attack, can I?

Thanks.