I have never used jiffy planters. I bought them once because I needed the heat mat. After reading reviews about them I decided against using them. That said I believe they're designed to transplant by transplanting the entire thing. If that's what you're going to do then you'll need to thin your plants down. If you want to prick them out then you'll need to have containers, pre wet seed starting/cutting mix or a good potting soil, and a tool such as a chop stick. I think there is a pro tool called a dibbler. I've pricked out 1000s of seedlings and rarely lose any in the process. If you feel the root snap while doing it then it's a goner. I start by using the chop stick and cut a little circle around the seedling. Then in a couple places stick the chop stick in and lift the seedling partially. The grab the seedling by the leaves and gently tug while continuing to lift with the chop stick. In the meantime the containers should be filled. Take the chop stick and make a hole all the way to the bottom and about the width of a dime at the top. Take the seedling and gently put it in the hole. Next take the chop stick and and insert it a few places to gently press some of the mix towards the seedling to avoid air pockets. Then use a hand sprayer and mist the container. Keep out of direct sunlight for a day. It may sound tricky but after a dozen attempts it gets fairly easy.

Check out the FAQ here on how to transplant.

Dave

Here is a link that might be useful: Transplanting FAQ