I've run split rims on my patrol since new (1980). You need a couple of decent tyre irons and a tool to go into the slot to lever the open end of the split ring to start working it out of the rim groove. The patrol tool kit came with the tool as part of the handle end of the lug nut spanner. All this AFTER you have broken the bead, so a bead breaker is the #1 tool to invest your $ into. There are various types of bead breakers from old school sliding hammer style to more modern and much easier to use devices. I use a pair of tyre pliers which work great on split rims.
I keep a few spare tubes in the vehicle, tip top/rema repair kits with various patches for repairing the tubes AND to repair any major holes in the tyre carcass. Also keep a couple of spare valves and nice metal caps (the type that can be used to also remove the valve). A valve tool is handy to screw onto the tube's valve stem to pull the tube through the hole in the rim and to keep it from slipping back into the rim/tyre. Make sure to have 'fresh' vulcanising fluid on hand - I prefer to have a bunch of the small 5g/10g tubes (sealed new until used) on hand versus the larger cans that invariably are all dried out after a couple of years in the back of the vehicle.
Some talcum powder in a small container/bottle is handy to rub over the inside of the tyre and the tube when re-installing. Decent rubber mallet doesn't hurt to have on hand to beat on the tyre to help re-seat it onto the bead if it becomes 'stubborn' while carefully re-inflating.
Bastard file if there's corrosion on the split ring surface and needs a bit of a cleanup.
I have all the above and other tools and stuff in the back of my patrol at all times.
Pair of mechanics gloves isn't a bad idea either. Oh, if you run a diesel, then some metho or petrol etc is handy to clean the surface of the tube/tyre if trying to vulcanize a patch on. Also the patch kit should have a roughening tool to roughen up the tube/tyre surface prior to cleaning and coating with the vulcanizing fluid. Kit should also have a tool with a 'wheel' to help work the patch and help with the vulcanizing/bonding.
That's all that comes to mind at this instant. It's 2nd nature to me when I have to repair a tyre, so trying to remember everything and write it down means I may have missed a few things...
cheers,
george.