The fastest method would be to find a yarn shop in your area (not a major store like JoAnn’s or Micheal’s, but a specialty shop) and see if the ladies there can help or know someone who can.
You can also try the method Gaspacho suggests, but this will only work if it’s a small hole in a sweater that has a fair amount of slack. Otherwise, the fabric will pull oddly.
If you want to try it yourself, you can probably manage if the holes aren’t too big and the pattern isn’t too complicated.
First, go to walmart or a craft shop and get a crochet hook. Ask someone if you’re not sure what one is. Go for a smaller one so you can be sure to get it into the knit of your sweater. A bit thinner than a pencil should be fine.
Find the loose, broken ends of yarn on either side of the hole. Tie the matching ends together. This part can be tricky if there are multiple broken ends. Be patient.
Now you should have a line of yarn going straight across your former hole. At this point, you have to recreate the knit pattern. If you look closely, you’ll see that each line of knit loops around the line above and below it in a series of U shapes. Sometimes the bottom of the U is on the side of the fabric that faces you and sometimes it’s on the side away from you. Also, at one end of your hole should be a strand that is complete, but that has too much slack in it. This is where you want to start.
Using your crochet hook, poke underneath that undamaged but slack line and reach up and grab the first repaired line. Pull the first repaired line through towards you. If the bottom of the U you just made in that undamaged line is on the wrong side of the fabric, flip the whole piece inside out and try again.
Keep going, each time reaching underneath the line you last had and grabbing the one above. Be careful not to let the chain drop and unravel the work you just did. When you reach the top of the hole, repeat with the first intact line at that side. Now, you’ll have a leftover U of line that has to be secured or the repair will undo itself. Use a piece of similarly colored thread and carefully tie the last U to an intact line nearby.
Be sure that the loose ends from your repaired lines are pulled to the inside of your sweater where they won’t show. Your crochet hook is handy for doing that.
You’ll have to massage everything so that the fabric doesn’t pull weirdly at your repair site. Just be patient. You have enough slack in a sweater to make it work.
Depending on the size if your hole and how small the knitting is, there may be multiple columns of U shapes that have been disrupted. If you can post a pic of the damage, we can help. Otherwise, see if you can puzzle it out. You probably can 
A pic will also show if the broken ends have snapped back across the knitting, which will be more complicated to repair, or if there is an ornate pattern to the damage.
Good luck!
