Careful basting of the quilt beforehand is absolutely essential so the quilt layers won't shift during freehand movement. Click here for a few basting tips before you get started.
First, you must prepare your machine. Not just any presser foot will work--you will need to install a darning foot. If you don't have one, check with the manufacturer of your machine to see if they make one. Lower the feed-dogs on your machine. This will allow free movement of the fabric as you push it around with your hands.
I recommend using the regular straight stitch with regular thread tension, as well as activating the "needle stop down" feature on your machine. (This will keep the needle down in the fabric when you need to pause.)
Position a corner of the quilt onto your machine. Lower the presser foot down onto the fabric. (If you step on the pedal, the needle will land in the quilt and stay because of the "needle stop down" feature.)
Using both hands, move the quilt around in a random swirl pattern. I make frequent pauses to adjust the surrounding fabric, remove safety pins, etc.
I recommend starting with the top of the quilt and moving down one row at a time (or whatever makes the most sense for the project--the idea is to do it in sections). Also, don't let your quilt hang over the edge of your table--the weight will pull on your machine's needle and cause unnecessary tension and make it a lot more difficult to move around. Keep it propped up on the table (or at least on your lap).
Here is a short video to help show you what the process should look like. (Do not feel the need to go as quickly as I do--that is how fingers get run over and quilts messed up.)
Practice, practice, practice! Before you attempt this on the quilt you have been laboring over for weeks, practice on scraps until you feel comfortable. Also, check the back-side periodically to make sure it hasn't bunched up. (Your careful basting should prevent this.) Should bunching occur, you will need to pick the stitches out, smooth out the area, and resume.
When you are finished, you will have a fabulous-looking piece of work!