how do you keep a dog from going into some parts of the garden?

I got some "indoor/outdoor" repellent in a red, white & blue can at Pet-Co a couple of years ago to keep Max away from the Christmas tree and it worked great.  Since it's also for outdoors, I don't see any reason why you can't spray it on the ground where you don't want him to go.
 
Joyce

or a hot wire. You can't really train him to not go there otherwise. He doesn't think ahead.

Paula

Get some visible barriers.   String between stakes with little flags that wave are good.  Always,,,, ALWAYS take the puppy out on line.  After the puppy has eliminated, then train the boundaries. 
Allow the puppy to move toward the barrier.  Step on the line to restrict the movement into the forbidden zone. 

Wait for the puppy to look back at you (wait for it, it will happen).  As soon as the puppy looks back, get silly,  jump up and down, call the puppies name in a happy voice, crouch down with a favored toy or treat. 

When the puppy gets to you, make a big fuss, pet and praise and touch and make the puppy feel good for at least 20 seconds.  Stand up ignore the puppy and repeat the procedure.    Do the activity 4-5 times each time you take the puppy out. 

When the puppy starts anticipating that you will be stepping on the line, start another type of boundary training.   Continue with the long line training, just add the other step. With the puppy on a shorter line (4-6 feet or so), start walking with the puppy around the areas with the barriers.  As the puppy strays toward the boundary,  move away from the boundary with the leave it command.  Make sure the moving away is fun and engaging for the puppy. 

Select a leave it command.  As you are walking the barriers (it may be helpful to do a random pattern including weaving toward the barriers) use the leave it command as the puppy is walking way.  Doing this quickly with skipping and jumping etc, can make leave it more of a fun game.  Leave commands should be rewarded with something as interesting as what had originally taken their attention from you. 

The leave it command can be generalized to other things in the future.

You can get an exercise pen. That's what I have.

If your dog is a digger, you can also create a special digging area - maybe fill in a small area with sand.  Then you can hide some bones in the digging pit and "help" the pup find them.  If he digs elsewhere, redirect him to his pit.  The intermittent reinforcement he gets from finding the bones, plus the fact that he never gets anything good in the other places, will help him confine himself to the pit.
If your pup is finding "goodies" though, in the places you don't want him to go (this can be anything - like cat poop, or bugs, etc.) then this training is not as easily accomplished, and you should supplement with boundary training, as mrv suggested.  Sometimes, you just have to get them over the puppy hump, and they aren't so interested in those areas when they get older (unless, of course, you have a terrier).

Just constant uh uh's.  All of ours stay out - even with wildlife tatunting them.  We didn't do anything special other than to say no, uh uh,  when they went in there.  Chloe was a puppy this past summer, so  i did put up a small iron fence (12") along the impatiens bed to keep her out.
 
Edited to add that you can see the garden behind them in my avatar.