Be very careful when removing the ring gear. You can usually just knock it off from the back bit by bit working your way around the ring. Be careful not to damage the cast iron flywheel which is not good at taking shock loads. Safest way is to drill a whole through the body of the ring gear, i.e. the area between the tooth gap and the inside diameter of the ring. This area is not hardened like the teeth. Then use a cold chisel to split the ring gear at the point where you've drilled the hole.
I concur the advice about chilling the flywheel and heating the ring gear. Best way is in an oven to get an even heat through the ring. You need to make sure you don't get it above about 250 degrees centigrade as this temperature will start to reduce the hardness of the ring gear teeth thereby significantly shortening their life. The worst way to heat the ring is likely to be with a torch because of the difficulty of getting an even heat and avoiding softening some of the ring gear teeth. You'll still get the ring on the flywheel O.K. with a torch but the effect of softening the teeth in one particular area will not be noticed from some months.
Some ring gears should only be fitted on one way. These have a chamfer on the end of each tooth to help the pinion slide into engagement. Make sure you fit them the correct way. Other rings have a larger chamfer on one side of the inside diameter. The large chamfer helps the ring slide onto the flywheel and sits better on the machined shoulder of the flywheel.
Most ring gears though can be fitted on either way.
When the ring is warmed place it on the flywheel, it should drop on fairly easily but may need tapping down during cooling. Make sure it is firmly against the shoulder. Use a feeler gauge of about 0.015" to check the gap between the ring and the shoulder, if you can get the feeler between the two in one area then tap the ring down with a copper headed hammer or an ordinary hammer with a soft metal block (Alumium, copper, brass, etc). You don't want to apply a hammer directly to the hardened teeth of the the ring gear. Typically the teeth are around 50 Rockwell hardness, but can still be damaged with a hammer.