How would i go about starting up archery?

I doubt what you are asking is legal. You need to find a local archery range. To start, visit you local sporting goods store and ask for information. Don’t expect the clerk to know, but the better stores have at least on person who can answer your questions.

In my state if you are using a bow with more than 30 pound pull you need to be at least 500 feet from a structure or residence. Surprisingly the same rules that apply for a shotgun.
The new compound bows: Bowtech, Diamond are extremely potent. They are not the same bow your grandfather used. You really need to know how to handle them.

My state has the same rule as @worriedguy

Compounds are nice, but I prefer to go Robin Hood style. I have a recurve bow. Looks like this one. Harder to hold a draw than a compound, but I think they’re much more fun.

Make sure you get (or make, also fun!) a bracer to keep the string from snapping you in the arm. It’s not pretty.

I used a 35 year old, 50 # Bear. It has beautiful lines and grace. Unfortunately with a magnifying glass I could see crazing in the limbs and decided it was time to move on. A broken limb can be fatal.
I got a Diamond Liberty, put in a hot cam, 80% let-off, and my recurve days are over. There is no going back for me. There is no recoil, it is easy to hold a full draw, absolutely silent, every shot is exactly the same. It is an awesome piece of engineering.

Yes, make sure that your activities will be legal. As far as where to pick up a bow, you can find them at yard sales, sporting goods stores and at organized archery shoots. I prefer recurve bows, but as has been said, it is easier to hold a compound at full draw for a longer period of time – given equal draw weights. In any case, if you are buying a used bow, make sure that the limbs are not twisted and that there are not any cracks in the fiberglass. Also, get a glove or tab for your fingers and an arm guard for your bow-arm. I recommend starting out without a sight and shooting very close to your target. Maybe 15 feet at first and then slowly working your way back as you gain more proficiency with your aim. Your shooting distances should never exceed those in which you can hit your target every time. Once you get the hang of instinctive shooting, maybe move on to putting a sight on your bow, but it’s not necessary. With archery, the most important thing is shooting consistently… not getting the most tricked-out bow you can find. I shoot a 60# Kodiak recurve without sights and have taken 11 whitetail deer with it – one at 30 yards. If you plan on shooting targets most of all, I recommend using a bow with a lighter draw weight: anywhere from 30–45#, depending on your ability to pull it back and comfortably shoot it repeatedly. Be Safe and Have Fun!!
Cheers!
– Soar

I’d be very careful about buying a yard sale bow! If it’s a recurve there could be crazing like mine and that is very dangerous. I kept mine in perfect condition but it got old anyway.. It is now a gorgeous wall hanger.

Compound bows should never, ever be dry fired. (string released without an arrow) The energy level is so high it can damage the limbs that can be lethal to the shooter even after one mistake. Any high power bow should be examined by a professional before you pull that string back to its full extent.
You are handling something that has 50–100 ft-pound of energy -similar to many handguns.
My Bowtech Liberty will send an arrow right through a 150 pound deer without it even flinching. All the components are matched. The arrows must be the right length, stiffness and strength. Draw length, let off, pull, sight position, cable release pressure all need to be set for your body size and strength.
If you buy a used one with no preparation, best case it will not shoot the way you want. Worst case you can kill yourself by breaking a limb, shattering an arrow and having pieces fly into parts of your body.
Let a pro set you up.

I would look for clubs featuring archery in your area. I’m sure there are websites that can provide you with tips about equipment and legal issues.

Yard sale bows are just fine. Just make sure that the limbs are straight and that there are no cracks in the fiberglass. Give it a good looking over. Make sure that the string is in decent shape. If you’re thinking about buying one from a yard sale, have the owner shoot it a couple of times for you. I’ve been shooting for 30 years and have shot all kinds of bows… used/new – recurves, longbows, and compounds – not a one has ever broken on me. Doesn’t mean it won’t happen, but it’s pretty rare if you’re not shooting some home-made junk. A lot of the time, when bows break, it’s because the owner has modified it in some way. Use common sense, think safety first, follow your local laws, and there are zero worries.
All the best to you!
– Soar

Match the arrow to the bow. The first example is perfect. My bow shoots at 300 f/sec. It gets up to that speed in about 2 feet of travel. That calculates out to 700 g.
The right match
The wrong match