After piecing and sandwiching the quilt - you finally get to quilt it! To avoid weird stretching when I quilt on my domestic (at-home sewing machine) I always start my seams on the left side and work my way to the right. If I'm quilting in two directions I complete the entire top in one direction first and then move to the other direction. Top to bottom or diagonal lines, whatever that may be. It helps keep the top smooth, prevents wonky stretching and requires less pivoting on the machine.
A lot of domestic quilters use a walking foot. It helps prevent the layers from getting stretched as you sew, since the foot grips the fabric on the top with the feed dogs below, pushing the quilt sandwich through the machine differently. It also helps make the stitches more even. The trick to a walking foot is going slow and steady. That said, depending on your machine, you might not need a walking foot. Before investing in a new foot, test quilt a sample sandwich with your regular sewing foot to see if the sandwich feeds well and the stitches are even. I have one machine that I use the walking foot on and another that I don't.
Your batting will instruct you on how far apart it needs to be quilted. It is a different depending on the batting. Some require stitching every 10 inches, others every 4 inches. You can do closer but do not do farther apart than suggested.
This is the where you quilt only in the seams (ditches) of the piece work. Important to note - this only works well if the seams are close enough together. Most battings have instructions on how close your batting needs to be. If your seams are farther apart than batting recommends then choose another option. That said, this is by far one of the most simple quilting methods. Just straight stitch along the seams.
FRAME THE BLOCK
This looks really good with a basic block quilt - but can look awesome on a lot of other quilts too. The idea is that you stich around the edge of each entire block - inset from the seam about 1/8".
Another really basic quilting method is straight lines. Starting at the top of the quilt, mark a straight line across it and then sew it. Repeat down the whole quilt either using a foot guide to follow your original line or marking each line. If you aren't sure how far apart to make your lines start with the minimum required by your batting and then fill in. I like to do every inch.
Tip - if your top has lots of straight lines (think all square blocks) this might not be the method for you if those lines are wonky at all. One option is to follow the seams instead to make it less noticeable or to try a different quilt method.
DIAGONAL STRAIGHT ROWS
Same instructions as straight rows, except you do this on the diagonal of the quilt.
This option is one I find absolutely beautiful. It is similar to the straight lines but instead of straight you softly meander back and forth as you sew. Then repeat at your chosen interval.
The book Walking Foot is a great resource for various designs you can do on your domestic machine. Lots of patterns can be made using straight, wavy or a combinations of lines.
BUILT-IN MACHINE STITCHES
You can try zig-zag stitches or mini-wavy lines, depending on your machine there can be a few or many built-in-stitches. Some machines even have built-in stippling or meander stitches. I highly recommend grabbing some scrap fabrics and batting and making mini quilts to test a few methods on your machine. It helps you get the feel for your machine and for the different methods you like.
Hand quilting should be done with a heavier thread, about 28 weight. It can be really simple, done in patterns, or can be amazing added detail to add to one small section of the quilt. Hand quilting can be straight lines or it can follow a ton of designs.
Using yarn or a thicker weight Pearl Cotton thread, about 8 weight, take a single stitch in the quilt, knot it and cut the threads leaving some to show. There are various variations of this - one where you "X" mark it with two stitches. You can also tie off on the back of the quilt instead of the front. Repeat all over the whole quilt at desired intervals - making sure to at least follow the required the minimum amount for your batting.
(Video Demonstration by Jenny Doan, Missouri Quilt Co.)