All the info you need is here:

Steam Levels & xp
https://help.steampowered.com/en/faqs/view/1F74-BE45-3AAC-1B47

Steam Sale Trading Cards & Badge FAQ
https://help.steampowered.com/en/faqs/view/7238-6689-609B-881A

Steam Trading Cards can be used to craft badges once you have a set of trading cards you can craft a badge you get Steam Trading Card drops by buying games that have trading cards and by playing the game the cards will drop you should get all card drops within a few hours of playing at longest and the amount of cards that drop depends on how many cards the game has for example if the game has 5 cards 3 cards will drop and if it has 6, 3 cards will drop.

Crafting badges with trading cards gives 100 XP and a badge for a game can be made 5 times each time gives 100 XP and additionally a game with trading cards also has a foil badge which has 1 level and gives 100 XP foil cards are needed to make a foil badge and they are much rarer than standard cards so foil badges are rarer. When 1 badge is made you will recieve a profile background and a emoticon based on the game you made the badge for, you can also sometimes recive coupons that give you a discount for a random game on Steam but these will expire in a few days if you don't use them in time.

Every time you level up on Steam you're maxium friends list count increases by 5 and for every 10 levels you get a profile showcase. And for every 10 levels you level up on Steam an additional 100 XP is added to level up again. So Steam users who are over level 100 need over a 1000 XP to level up 1 level whereas users less than level 10 need only 100 XP to level up once.