I don’t understand how to use the points or get more points from discarding cards.
If you go look at one of your collections and hover over a card, you can see a discard button. When you discard a card, you get points corresponding to the rarity of the card. 100 for common, 200 for uncommon, etc.
You can use the points to buy more card packs – it’s 10k points for one pack. I personally wouldn’t recommend it, though. The odds are the same as with a free pack. It might be a much better deal to just trade away the cards for other cards you want.
edit: You can also get points from completing series. e.g. when you get all the commons of the series, etc.
Completing a set can get you enough points to buy 2 packs. That includes points for completing the rarities.