A dc is when you wrap the yarn around your hook, insert into next stitch or space (as directions indicate) then wrap yarn again, come back through stitch. You now have three loops on your hook. Wrap yarn again, pull through two loops on hook.
Wrap yarn again, pull through the two loops remaining. DC completed.
Half Double Crochet
A hdc starts out like the double crochet, but when you have the three loops on hook and wrap yarn, pull through all three loops. HDC completed.