How do teams get compensatory draft pics?

the same way they get physical

they let their bodies talk

seriously, there is this intrawebs thing https://en.wikipedia.org/wiki/National_Football_League_Draft#Compensatory_picks

We will get a compensatory pick next year for Bushrod, and maybe even 1 for Ellis

Essentially by drafting well. Teams get compensatory picks when they lose more players to other teams than they sign to their own... with some sort of differential in there to compare the size of contracts. While most Saints fans point to our success in later draft rounds and undrafted free agents, this team drafts extremely poorly in the early rounds and doesn't particularly value their draft picks... trading them away for mid-career veterans like Vilma and Shockey.

Now let's look at some stats, ignoring this latest draft:

From the last 7 drafts, we have kept 11 starters from 41 drafted players, and in the first 3 rounds during that period, we have kept 5 of 15. (Jenkins, Harper, Robinson, Graham, Jordan)

For reference, that's 2 fewer picks than Seattle in the first 3 rounds. 6 fewer than San Francisco. 6 fewer than Houston. 8 fewer than Baltimore. 8 fewer than the Giants. 8 fewer than Pittsburgh. 9 fewer than Green Bay. 13 fewer than New England.

What's it mean? The teams that are good and upcoming build through the draft. They trade down to get extra picks, use those extra picks to get as many good players as they possibly can, and when the picks leave for better money, it's all good because they're just going to get compensatory picks to pick up even MORE players.

Here's how bad it is for the Saints: the Patriots have drafted 25 more players over the past 7 years than New Orleans. That's almost half a TEAM. If you want to know which teams have the best foundations going forward, just look at their drafts. Simply by virtue of trading down and drafting well, you perpetuate the ability of your team to do well simply by allowing yourself perpetual access to more talent.

This season?

San Fran made 11 selections. Seattle made 11. Green Bay made 11. Baltimore made 10. Houston made 9. Pittsburgh made 9. Atlanta made 8. 4 New England made 7. Meanwhile, New Orleans made 5.

We aren't getting picks because we do a horrible job of judging talent in the early rounds and a terrible job at managing the draft.