Since cats love to climb trees, the first thing you should do with your tree this season is to make sure it is secure and won't topple. You can do this by looping a monofilament fishing line around your tree and putting a molly screw into the wall behind the tree and tying the tree to it. You can also tie the line around the top of the tree and tie it to a molly in the ceiling. This will prevent the tree from tipping over.
Then, you should leave the tree up for three full days without decorating it. It will be hard to resist the urge to decorate your tree, but this will allow your pet a good amount of time to get acquainted with it. Your pets can play with the tree until their curiosity is fulfilled, and hopefully by the time you go to decorate it they will be bored by it.
When you begin to decorate it, you should put the more delicate ornaments at the top, especially if you have a larger dog. Some big dogs have long, wagging tails, and you don't want them knocking your ornaments off and breaking them -- if they are glass ornaments, little animals could cut themselves.
If you have wooden floors, you could duct-tape the cord to the floor; if you have carpeting, you could go to the hardware store and get a piece of PVC pipe and run the cord through that. This should stop your dog from chewing on them.
Most important: Do not use tinsel if you have a cat. Cats love to play with it and eat it, and it is deadly. It gets stuck in their digestive system and could end up killing them.