There is a mother cat with kittens outside my apartment. The kittens are young. Eyes open but not 8 weeks old. What is the best approach at getting them safely to the shelter.

You can catch the call shelter to come and get them

Also, unless a cat bites someone, they won't usually come out for cats because the mother cat will be extremely difficult to catch.

Capture them and take them or try and call animal control but they will probably be busey with calls so no tell in what time they will make it out

If you call the shelter, I believe they will pick them up. If not they would need to be placed in a box or crate with the mother to take to the shelter. The mother would be the problem if she is wild. Be careful if you attempt to capture her and the kittens. I don't recommend it.