Premium Dust is as the name would imply the games premium currency, unfortunately there is not a lot you can do in the game to earn a significant amount of it. So unless you want to purchase it as an in-app purchase using real money you will have no other option but to grind for it if you want a good deck. Listed below are several ways in which you can collect free Premium Dust.
System Mail
If you open your inbox and watch the advertisement video you will be given a reward in exchange. The reward you get could be a Scrap Crate, Lien or Premium Dust.
Missions
Completing the different missions and their tasks will usually reward you with Crates, Lien, and even Premium Dust. The tasks you are given during missions are simple and every time you successfully carry them out you will be rewarded with 5 Premium Dust.
Daily Rewards
You will be given rewards each day that you log in the game. On the third log-in day you will be given 200 Premium Dust.
At the end of a match, you will receive a battle crate that must be opened with one of your keys. Accumulating Premium Dust is important as it will allow you to purchase extra keys. If you do not have any keys at the time of winning your match the crate will go to the waste. Premium Dust can also be used to purchase packages of Liens in the shop which can then be used to get the Bulk Crates which guarantee a pull of rare cards.