Having access from above (with the attic being above your kitchen) is very helpful.
You also said there's an existing light source: I'm going to assume there's a power source in the ceiling. If so, you can probably handle doing the job yourself.
First, you'll need to turn off the power for the area you are working on. Use a drywall saw to cut openings for the recessed lights (a drywall circle cutter is a very helpful tool for this as well - especially if you are installing several fixtures).
Make sure to locate the ceiling joists before you cut the holes - you need the recessed lights to go between the joists. An electronic stud finder can help with that. Be careful that you do NOT cut through any existing cables in the ceiling.
Here come the electrical connections: You'll need to insert the cable from your ceiling into your recessed fixture's junction box and fasten it with a cable clamp. This is where your product installation instructions will come in handy. Remember to match the colors: the fixture's black wire should be connect to the black wire in your ceiling; the white wire should be connected to white, etc.
Installing the housing, baffle and trim are a piece of cake once you have the electrical connections set up: consult your manufacturer instructions for this.
Good luck! You can always call an electrician if it gets to be too much to handle, but sometimes it's fun to try the DIY route.