The baggie method is an easy way to germinate the seeds.

Take a handfull of so of damp not sopping wet sterile potting mix or peat moss. Coir peat can be used also. Put it into a ziplock bag. Put in a few seeds(I usually place about 10 in a quart size bag). Mix to slightly cover the seeds. Zip it up. Place the bag on top of your monitor(if left on all the time), cable box, or other place that stays warm all the time. In 2 or 3 weeks you will see roots coming from the seeds that have germinated. I then carefully take the germinated seeds out of the bag and pot up into seedling pots. These are little 2"wide x 4" deep pots. Place these pots in a warm bright area and they will grow. I have some that were potted up a month ago and now they are 3" tall with 4 sets of leaves. You can start feeding the seedlings after they have developed their first set of "true" leaves. These are NOT the first ones that appear but rather the 2nd.Feed with a good fertilizer mixed at 1/4 the rate per gallon.
Hope this helps.

Key limes can be grown from seed to fruiting in 2 or 3 years.
Andi