How long do my baby's naps need to be?

Depends on the baby. It depends not only on the baby, but also on how well they're sleeping at night. If their nightly sleep is good - good length, good quality, sustained through the night - then they're daily naps are more dependent upon their particular needs, if they don't sleep well at night, though, daytime naps may be part of the problem. This is always a good one to discuss with your pediatrician.
Long enough. Babies, just like adults, vary in the amount of sleep they need. Newborns sleep 16-22 hours a day and this decreases as the baby gets older. As long as your baby does not seem overtired (fussy, not feeding well, not playing) and continues to sleep well at night, then s/he is getting enough sleep. For some this is 2 long naps a day, others it is 4 shorter naps, all depends on your baby.