When a teammate dies, go to their loot pile and grab their Banner, you have a 90 second period to retrieve it once the player is dead. When you have retrieved their banner, you must take it to a beacon, which is identified on the map with a green marker. Go up to the respawn beacon with the banner and a prompt will come up to respawn your teammate, you're pretty defenseless when doing this so make sure you check the area for enemies first. When you have uploaded the banner to the beacon your teammate will re-enter the fight through a dropship. Good luck!