If you know any arborists, you will notice they look up a lot. There is a reason for that - arborists, unlike most other mortals, are very interested in things falling on them. So should you be. If you're about to throw a rope in a tree, have a good look at the tree first. If there are any dead or broken branches up there, get a professional arborist to make the tree safe!
In the USA (or anywhere else) I recommend you use an arborist who is a member of the International Society of Arborists (ISA) or the local national body - in New Zealand, NZAA, in Australia, ISAAC etc.
Step 1: What you need
Have a look at this related link How to Climb a Tree (with prussiks!) - I am working on another instructable on tree climbing too :)
To set a rope in a tree you will need the following:
You need a rope twice as long as the branch is high (ie if the branch is 12m off the ground you need at least 24m of rope). You'll figure out why. Do NOT compromise on the quality of this rope - your life depends on it. Go for a polyester or poly-blend rope that has sufficient break-test to support your life. The IDEAL rope will be a rated, arborist's climbing line which will have a break test of around 5400lbs or 2700kg. There is plenty of yachting rope around that is strong enough - it just isn't break-tested. Polypropylene rope is also very strong - it's just a bitch to work with. OK for a swing, but not for climbing on.
This can be a commercial arborist's throwline (like Zing-it) or monofilament nylon or even sash cord or string. Basically, a thin, slippery cord that you can throw over a high branch. Good-quality throwline is easier to throw and less frustrating, and not highly-expensive, but you can cut costs here without compromising your safety.
The best throwballs are made by commercial arborist's suppliers. Arguably the best throwballs are made by Andy Harrison in NZ (firstname.lastname@example.org) and you can order them via e-mail. They're not expensive, and they work really well. Throwballs are filled with lead shot so they're soft but fairly heavy.
If you're a cheapskate you can throw any heavy object you like over the branch. I don't care if you choose to throw a piece of rail or an anvil - just remember when it comes down it can hurt you. I am not responsible for damage that you inflict to your neighbour's glasshouse or Porsche.
Wear a cycle helmet, a skate helmet, or a climbing helmet. Then the anvil falling on your head won't hurt as much.
A cambium saver
You don't really need a cambium saver. But if you're climbing in a tree and you want to set a rope, use one. It saves the bark, and it makes it easier to climb the tree, and it's easier on your rope. I'm just showing you the right way to do it. I appeal to your deep-green moral conscience.
A cambium saver is a rated load sling with two rated metal rings at either end (pictured). You can improvise one from a load sling or a loop of rope and carabiners, but make sure that everything you use is rated.
Gear advice - never scrimp and save on climbing gear. Find the best price for the good stuff. There are heaps of commercial websites. Start at www.petzl.com and work outwards.