First of all, it's important to know what exactly are DeviantArt points?
DeviantArt points are a currency that is used on DeviantArt alone. In this website, you can buy points, you can get them, collect them, and buy things for them. It's basically the DeviantArt equivalent to money. Which might come in useful because even for those that don't have a credit card or Paypal account, it is now possible to get a premium membership. Points can be either bought, or gotten for free from other members. There are many ways to get them. I will list a few here.
Most obvious one: Buy them for money. You need credit card or Paypal, though.
Trade them for llama's. your-username.deviantart.com/badges/ will list people that'll trade llama's for point on the right side. Give that person a llama, and you'll get some points. It's as simple as that.
Open up a donation on your page with the donation widget. So people that feel generous can give you some. It helps stating what you use the points for. For example: a premium membership, contests or giveaways.
Do point commissions. You draw, and people will pay you in points. It's as simple as that. Remember. 1 point = $0.01. So make sure you don't sell yourself short.
Join giveaways. The journal portal often lists many giveaways in which the prizes are points. Rules differ per giveaway.
Join contests. Prizes are often in points. Rules differ per contest.
Bots like dAhub or dATrade will give you points for watching, faving and giving llama's to people. While this might seem unfair to some, it's certainly a way to collect points more quickly. And it might be even a good way to discover new and unknown artists.
Anyhow... happy point collecting!