“So, simply put, how do you get your page to show up higher in people’s google’s searches?”
There is no simple answer. You have to do many things.
“Then I thought it was with getting people to link back to you by exchanging links. Then I found out this is only like trading soldiers and can actually end up hurting you.”
Things are not simplistic. Exchanging links can have value as I mentioned above, but generally not from a pagerank perspective. A positive on one side of the ledger might lead to a negative on the other… like paying for an ad, you have to pay, you don’t get it for free, but you will either decide the ad is worth it overall or it isn’t.
“It can only help if you’re exchanging links with someone who has a larger PR than you”
In terms of PR yes, in terms of rankings, no. A higher PR link page getting a lower PR link from a topically relevant main page could make perfect sense and benefit both sites.
It’s a stew, and fiddling with the ingredients can make it better (or screw it up completely).