The fastest way to level up is by crafting badges.

You can also:

• Earn the Community Badge by completing tasks.
  
• Redeem Steam Points for the Seasonal Badge.

Here's the FAQ for Steam Levels and XP.

There are a few ways you can do this, some cheaper, some more expensive.

When you play a game, it gives you trading cards, usually around 60% of the total cards for that game. You can buy the remaining cards on the Community Market. Once you have all the cards, you can craft a badge that gives you XP. You can craft a badge for a game up to five times. But the number of cards a game gives you is limited, once you’ve received them all, you’ll need to buy the rest on the Community Market.

When you spend money on Steam, you earn points in the Points Shop. On top of that, people can also award you points for comments, reviews, guides, and other community contributions. Inside that shop, there’s a “Seasonal Badge” option, which costs 1,000 points per level and can go up to level 40.

It’s also possible to farm the “Community Leader” badge, which is completely free, you just need to complete some missions within Steam. That badge can give you enough XP to reach around level 10, if I remember correctly. You can check what missions you still need to complete and your progress in the badges section of your profile.