pre reboot: 

Dick became robin around 10-12 years old when his parents died doing their trapeze act. He grew up, moved on to nightwing at 19 and 13ish year old Jason became Robin. Jason (parents: mom died with him, I think two-face killed his dad) got killed at 16ish and when he did, Batman became very depressed. Tim Drake, who had been stalking Batman/Robin since he was four, saw that Batman needed a Robin and kind of took it upon himself to be Robin at 14. At 15/16ish, his father found out so Tim quit and his girlfriend, Stephanie Brown became Robin at 16 I want to say. Tim’s mom died when he was a kid, his step mom had break down (oops, not died, thanks anon) after he became Robin and his father died after Steph died.

After Steph got killed in War Games (boo), Tim became Robin again. Steph’s father is a criminal and he’s in jail. Around this time Jason comes back to life as the Red Hood and later after that, Steph comes back to life too. She lives with her mother. When Bruce Wayne died, Dick saw that Bruce’s son Damian Wayne (10) needed guidance and direction so he gave Tim’s title to Damian. Tim was understandably upset and still mourning Bruce so he became Red Robin while Dick became Batman and Steph became Batgirl. 

post reboot:

who cares, don’t listen to them, make your own head canon, four robins in five years is bullshit, long live the short pants, also there are five robins, shut up DC, etc.