Step 1 Edit
Find a wild wolf (just any old Vanilla Minecraft wolf)
Alternatively, you can automatically spawn a tamed dog by using the "Doggy Charm" item that comes automatically in your inventory bar when you start a game with this mod installed (as of version 1.7.10 in April 2015).
Step 2 Edit
Feed it bones (right click with a bone in your hand) until hearts appear above its head. If a collar appears on its neck and it sits down, you've done it right!
Step 3 Edit
Feed the dog at least one Training Treat! Now, you will be able to right click on your dog with a stick in hand to open the training menu!
So that is that and you can now go train your dog and get it ready for an adventure