Aresol carb cleaner, an ice cream bucket of gunk cleaner, various screwdrivers and pliers, and lots of shop towels and elbow grease are all you should need--unless you are also in need of some non-metal replacement parts like o-rings or gaskets.
My basic tenets of carb cleaning are:
1: Make sure that all of the fuel *metering* passages are fully clean and clear. This includes all of the very small holes in the sides of any emulsion tubes and various jets--if you can't see daylight through them, they are not clean. These are the openings that gasoline must pass through as a liquid, that breaks up the liquid stream into tiny aresolized droplets. Because of their tiny size, they are absolutely the most likely to be clogged, and once clogged, no amount of hoping/wishing/swearing will fix the problem. Small wires, spray cleaner, compressed air, soaking in a small container of cleaner--all of these are options when cleaning jets and tubes.
2: If the parts of the carburetor that you are considering soaking don't usually live in liquid, be very certain that nothing you put in to soak will be damaged by doing so. O-rings, gaskets, and other soft materials tend to "grow" when exposed to certain liquid chemicals, making them another source of frustration. I have found that soaking is rarely needed, but can sometimes be necessary.
3: Take apart all of what's necessary to address the issue(s), but nothing more. Sometimes people take *everything* apart for the sake of doing a better job. Remember, carburetors that were once working just fine have not put themselves out of adjustment. The usual cleaning needs are limited to the bowls and slides. The bowls (jets, floats, etc...) will be likely the victim of crud from evaporated gas. The slides live higher up, out of the way of standing liquid gas, and will be the victim of corrosion that locks the slides in their bores. The fit is so close between these moving parts that they can hang up or get stuck fast quite easily. Of course, leaky fuel inlets and mixture screws must be addressed, as well as vacuum diaphragms on CV-style carbs.
So, in short, get after the slides, bowls, jets, emulsion tubes, needles and seats with careful attention to detail, and your problems will likely be addressed.
All the best,
Shane