How do I grow levels?

^ This

Buy a TON of games or waste a TON of money on pointless badges. It's a giant cash grab for Steam, even community events (like the summer one) require spending money now (and a lot of it). To reach the highest level in this community event (level 5 badge + foil) you would have vote in every 8 hour poll to get about 13 cards PLUS find 47 more. You could potentially sell your cards from games for those, however you're going to need to play at least 94 games with 5 cards each and get a 1:1 trade/value ratio... and that probably won't happen so what Steam is banking on you doing is dropping money into your Steam Wallet (getting it into the Steam system, so it gets spent there) buying the cards and then whoever sold you the cards buying TF2, DOTA, etc items ideally; though they'll settle for games they get less profit that way.

TL;DR: You have to craft badges by buying games and collecting/trading cards OR drop tons of money on Badges that provide no benefit besides to you besides a badge and profile level on Steam; the system is a big cash grab by Valve.

Also, upgrade your Community Badge

http://steamcommunity.com/id/archlion/badges/2

Each level up to 10 is 100xp. Up to 20 is 200, and so forth.

I took a look at your profile. You can get the Community Ambassador badge by upgrading your Pillar of Community badge to the next level. You don't need to do ALL of the tasks, just 22, so you don't need to spend any money.

I think all that matters are the number of games in your steam account. With badges like power player, stuff like that give you a ton of XP.