When you're sewing in knit fabric an overlocker or serger is great to use. But it's not necessary and you can achieve really nice results with a regular sewing machine too.
Use the correct needle
The most important thing is to switch out your universal needle on the sewing machine for a ballpoint/jersey or stretch needle (B). They have a rounded tip which won’t ruin the fabric. The same goes for your twin needle, if you’re using one. That one should also be ballpoint/jersey or stretch (A).
Use a stretch stitch
This is really important, especially for horizontal seams where stretch is needed (e.g. the neckline). A seam that doesn’t require much stretch, e.g. vertical seams such as the side seams, can be sewn with a narrow zigzag stitch.
A: Overlocks seam, for that you will need an overlocker/serger.
B: Narrow zig zag stitch (approx. 1,5 mm wide and 1,5 mm long).
C: Wide zig zag stitch (approx. 2,5 mm wide and 2,5 mm long).
D: Twin seam (switch out the needle for a twin needle, and use a stitch length of approx. 3).
Don’t pull the fabric
Try not to pull the fabric as you’re sewing. That generally results in a “bubbly” seam. Neither should you let the fabric hang down from the table. Lift it up so that it can be easily fed into the machine.
Always press a seam after you’ve sewn it. Don’t wait until the entire garment is finished. Pressing is often the thing that takes away that “homemade” look and gives the garment a professional feel. When you’re pressing, the thread “melts” into the fabric.
Use a walking foot
If none of the above helps you could try switching to a walking foot (C) instead of a regular presser foot (D). It keeps the fabric from stretching as you sew.