Go to Cards and then click on any card. Once there click on Stats. That shows you how many cards you need of that particular card in order to level them up. For commons it's usually 5 for level 2, 14 for level 3, 30 for level 4, 60 for level 5, and 100 for level 6. You need to acquire that many cards and then combine them to reach those levels. There's a little "combine cards" button in the row of icons which include renting them out, selling them, etc.
The BCX number is how many cards have already been combined to make the card you're looking at. BCX stands for "Base Card Experience" or something like that. Each BCX stands for one card. So if you look at the market and see a level 2 with a 5 BCX, that means someone has already combined 5 of those cards to create the level 2 card. You could then add 9 more cards to that one if you want and turn it into a level 3.
I'd recommend doing it once with the cheapest card you can find just so you know what you're doing. That Spinner that's being given away here is a pretty good candidate. It's pretty cheap IIRC. It is also a card that has it's uses. Especially in certain rulesets or in low mana battles.
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