When do you get an assist in Apex Legends?

Is it based on the amount of damage you've done or something else?

Respawn defined assists for season three:

Assists are defined as dealing damage to a player within 5 seconds before they are knocked down. If a player is revived, the assist credit is cleared. Assist credit is only given to teammates of a player who earns the kill. A player cannot get a kill and an assist on a single opponent.

Then they adjusted assists for season four:

We have, however, adjusted assists. Firstly, we changed the Assist timer from 5s to 7.5s. Next, before Season 4, when a player finished using a healing item (e.g. syringes/shield cell etc) they would clear any assist credit. This was unintended and has been fixed. Mirage's Decoy Trigger, Crypto's EMP and Pathfinder's Grapple now give assist credit for the standard 7.5s after activation, even if they deal no damage. Bloodhound's Scan and Crypto's Passive now give assist credit if a player dies while having that status effect on them; and for 7.5s after the status effect runs out.

Yeah it would have to be only on active fire while your teammate actually secures the kill. They really don't like dishing out assists in this game.