(Xbox control scheme)
Press start to open the menu, in the upper left you get a window which shows various statistics. Toward the bottom of this window is mission pass details, including present season and the tier you've presently reached.
Press X to see your mission list from here. Of these, Daily Missions, Weekly Missions and Tier Missions all show as giving tier points (the yellow star on a purple square). Tier Missions give the most by far, but like Weekly missions seem to be time-limited with the present season already half over.
Press X again to see your mission pass directly. It'll show your tier and any rewards you can claim. You need 10 stars to advance in tiers and you level automatically.