Are you using a separate flash unit? In that, is mounted on the hotshoe? If so, I have an idea for you that worked well for me when I just began. First, get the flash off camera--this can be achieved with the following cord, or one of similar make (the one I linked to is designed for Nikon camera's).
Vello TTL-Off-Camera Flash Cord for Nikon SLR - 3' (1 m) OCS-N3
Next, grab a shoe box or something similar. Line it with tin foil, and cut off one of the broad sides (the top or bottom). Place your flash in one of the sides, with it pointed towards the inside of the box, and cover the open side with tissue paper, wax paper, anything that will diffuse the light.
Next, hold the flash off to the left or right (whichever is more comfortable), and shoot! You'll see hugely improved results. Below is an image of a similar device I made, and then a self portrait I took with it, holding the flash, aimed at myself.
Best,
Jake
P.S., if you don't have an off camera flash, you can buy used or third-party for easily under a hundred dollars.
Edit: Also, the actual cost (if you already have a flash unit) is easily under 30 dollars. So it's simple, cheap, and pretty damned effective. If you want to get fancy you can make it out of plasticore (
http://www.coroplast.com/catalog/Files/Images/Plasticor_White_Cap_Small.jpg) and make the front with a thin white sheet. It's really easy to cut, can be had for about $5 a sheet at Home Depot, and will hold up much better than the shoebox.