get a
shop manual
that's an actual honda shop manual for the cb360, from honda issued to dealer shops. I have one and its awesome.
Next I'd pull the carbs and do a rebuild and very thorough cleaning.
Carb rebuild kit
Also, I'd do a compression test on the engine (if its not seized up) and see if you have good compression, the manual will have what the compression rates should be. I think its like 90/140/160/170/170 (psi). Use the kick start with the compression tester, you should have something like that for each kick (90psi first kick, etc).
Here an ebay link for a
battery box and
petcock
I'd get some new spark plugs and a battery, if the compression test is good, and you've got your carbs all cleaned up I'd try to fire it up and see if it runs. You might need to work with the floats a bit to get them right and I'm pretty sure you are going to need to get the carbs sync'd up, but the bike should run without a sync, just maybe a bit rough. If you get it running do an oil change. I'd do it after you get it running 'cause if you do it first and you have to tear into the engine, then you wasted an oil change. The filter is inside and doen't really get changed. You can clean it, but its a non disposable centerfugal filter and its inside the engine and is a real piece of work to get at. The manual will explain. Do clean it before you really start to ride though. As for oil, I use mobil 1 10w40. The book says you can use sae30, 10w30 or 10w40. Mine always seemed to run hot on the 30 that was in there, so I went to the 10w40 and that seems to work better.
After the bike runs you can worry about setting the chain tension, new tires, electrical issues, all that other fun stuff. There's a coil power mod that you can do that really helps with ignition. But you can worry about that after the bike is running.
Oh yeah,
fork seals
And you can get mufflers from JC Whitney, they aren't quite stock, but they look good and they are WAY cheaper than finding some NOS exhaust.
Have fun! I have been working on my CB360T for almost a year now, its been frustrating at times, but very rewarding when it works out. When I ride around on it I always get compliments on having an old bike that looks good. When working on a bike like this i've found that ebay is your friend, as you can find most of the parts you need on ebay, just be careful. Any other questions just ask...this place is awesome when it comes to help.