10 month old still not sleeping through night

Betthany • Stay at home wife and mother. Married my best friend Nick 6/28/14 and gave birth to our son Noah 1/4/15.
My son is almost 10 months and still will not sleep through the night. He wakes up multiple times. I've tried to give him a few minutes to soothe himself back to sleep before rushing over to him. I never let him cry really, i usually only do this if he's just fussing a bit. He seems to think he needs to lay on my chest to fall asleep and when we try to transfer him to the crib, h3 wakes up screaming. We've even tried to let him fall asleep on his own, when he's visibly drowsy but not fully asleep. I'm really just asking for any and all advice you ladies may have as to how to get him to sleep longer or better on his own. This mama needs some sleep and so does the baby!