At what age should I begin training?

Every interaction with the puppy is "training" in one way or another.

You can start teaching a puppy simple things without formal "commands" from a few weeks old.

At seven weeks old, I would work on things like:

follow me
come to me
watch me
lay quietly and let me stroke you ("settle")
let me play with your feet, tail, ears and teeth
let other people greet you and touch you
interact appropriately with other puppies
and start teaching the pup's name (when you say it, if he turns his head to you, reward that)

Keep "training" at this age short and upbeat. after 10 minutes you'll have lost their attention completely.

Re: Thanks!

My little girl is 10 weeks old. Today, we were working on sits, downs and come. She LOVED it. Pieces of kibble (which was her lunch) to run to Mom. Wahoo! I love Mom! I love my kibble!

Bits of Cheese? To plop my butt on the floor? Wow! What a great gig this is! I could do this all day!

And what's this? Mom's holding a piece of treat between my front paws? If I just lie down, I can reach it. Oh wow! I get the snack and Mom's thrilled. Hooray for me!

I don't see ANY reason to wait. Yeah, we're potty training. Yes, we're socializing. And yes, she's doing sits and downs. And she's scoring nice snacks for it.

As Tracy says, we keep training sessions brief. And I scatter commands throughout the day, so she learns things as she moves through life. Before we cross the street to get the mail, when she's on a leash, we stop, and I tell her Wait. She doesn't understand now. But slowly, she'll learn it without my ever formally training it to her.