I do not know how to check transmition oil in my land rover lr3

Leaking from where and how bad is the leak? If only minor, get under the vehicle and check for signs of leakage at the drain plug and around the oil filter - these are the most likely culprits. If not obvious, clean everything up, drive and look again.
If these places are not the source, (assuming this is a petrol model) look at the rear of the engine from the top and from underneath in case it is a leaking head or valley gasket

This has to be done by a Land Rover service dealer.

it is time for an alternator,,,real common in the lr3.

It can come in underneath, through the floor. Also the cables that go between the door pillar and door can permit water to pass, if they are not sealed correctly.

some of these cars have a plug near the trip meter reset that is pressed with a long narrow object like a thin Philips screwdriver or a knitting needle.

That little ship means you are low on coolant, check the overflow bottle for the antifreeze.

Did you take it to a rover dealer?. If not, it may be worth it.

Service light reset – Land Rover PDF File

I hope helps with this (remember rated this help).

This link may be of help to you

http://www.keylessride.com/keyfob.asp

Read the vehicle manual or spend some time under the hood to locate anything that looks like a metal flower growing out of the engine with a loop to pull it upwards.