Sure Rebecca! I'll tell you what worked for us, and then follow that up with some links to discussions where others have offered their advice.
We got Sidney as an older puppy (5 -6 months old) so he already was taught not to bite. They say the longer a pup is kept with its mom and siblings, the less likely he is not to bite during play. Puppies sold too soon (6-8 weeks) are more prone to it.
Sidney would occasionally get too excited during play. When he would use his mouth (even if it was not a bite or nip) on us, we would emit a high-pitched "yipe", similar to the noise you'd imagine a puppy would make if it was hurt, and turn away from Owen. Go back to play and if he does it again, repeat.
Don't use a muzzle hold, that will make a determined type corgi try harder. When you say something negative as a correction, avoid using "no" because it is used so much in normal conversation. Most people use some form of "ack", very harsh sounding word. It was weird to use at first but it is effective, and sometimes I find myself using it with my kids or nieces/nephews!

As for nipping at your heels when you walk, I'd suggest you use what you read in these discussions; I never had to correct Sid on this type of behavior:

http://www.mycorgi.com/forum/topics/1150197:Topic:44132

http://www.mycorgi.com/forum/topics/1150197:Topic:117729

http://www.mycorgi.com/forum/topics/mouthy-little-jasper

http://www.mycorgi.com/forum/topics/1150197:Topic:100138

http://www.mycorgi.com/forum/topics/1150197:Topic:77230

Good luck, and let us know how he's doing!

Hello Owen and Mommy!