Don't take the taxi. It's a waste of money. I think it's a flat rate of like $50 bucks to get from the airport into the city. But worst is renting a car. DO NOT DRIVE IN NYC. First and foremost, most likely there will be better instructions so check with the transportation desk when you get there. However, this is how I would do it. From JFK, take the airtran inside the airport to the Jamaica Center. It's the last stop on the airtran, you can't miss it. From there, take the E Train west. Depending on where you're going, you'd probably want to get off around Rosevelt Ave. From there, you're not far from Lagaurdia, but it's still a little bit north of you. However, I think Rosevelt Ave is a good spot to get off because you can transfer there to other subway lines.
Here's a link to a subway map that can help you.
http://www.mta.nyc.ny.us/nyct/maps/submap.htm
If you tell me more info about your hotel I might be able to help you out, but this is all that I can tell you. It'll cost you $5 for the airtran and about $2 for the E Train (which is part of the subway system). When you change trains (subway, whatever you want to call it) at Rosevelt, it should cost you nothing, but I don't know where you're going next. Thus, the total so far should be $7. At worst, from there you should be close enough to Laguardia where if you need to take a cab, just get one. It won't cost as much as getting a cab at an airport and there should be a meter.
Good luck and let me know if you need anymore help. I fly into JFK pretty often and into Laguardia once. But I've been in and out of NYC pretty often. I'll let you know the cool place to go to if you need it.