First - start with bullet proofing the case that it is a problem. I don't mean to sound cynical, but the number of times that employees have brought me this situation while using a company specified machine that is rarely a problem is about 50%. Make sure that any extraneous software is not automatically provided and not needed to do work is removed. That includes IMs to the outside world and close windows hosting anything streaming. Also be sure that this is generally a problem with anyone having a machine of your type, and/or that your machine is of an incredibly ancient variety.
If you've done all that, fantastic, sorry to be a pain and ask...
A proper way to tell them whats my problem?
1 - Know the comparison. If you are doing a job done by others, know the specs of their equipment and have a case for why yours is worse. "My machine is the 2009 model, and everyone else in the office was issued a new machine in 2011", or "I have half as much RAM as everyone else in the office". This is a much harder case to make if you have the nicest, newest equipment in the building than if you got the horrible leftovers.
2 - Know what your tools require - particularly if you are the special guy with the special tools - then know why your tools require more. "I'm using the XYZ tool, it requires X RAM, Y hard drive and a CPU of Z, and recommends XX, YY and ZZ -- I have less than X, Y, and/or Z which isn't supported by the vendor"
3 - Know the true impact and describe it with meaningful specifics. For example
The slowdown due to poor equipment occurs every time I start the XYZ tool. Starting the tool takes N minutes, and I must start the tool every morning/after lunch/every 30 minutes, etc
I can't use X tool and Y tool at the same time. Starting and stopping the tools causes slowdowns when doing task A which requires at least 10 cases of switching back and forth. What should take 30 minutes then takes 2 hours, and I do this task every day...
The system runs so slowly that a rebuild that would take 5 minutes on my coworker's machine takes 30 minutes on mine. Our coding environment is one where we rebuild multiple times an hour. While the code rebuilds my screen freezes making it impossible to review or research anything else while I'm waiting.
Don't go lower than this, but give the math that allows your manager to add it up and say "wow! This guy would be able to do twice as much if we gave him decent equipment".
what should be the matter in mail so that my request should get approved?
There is no final answer on this part.
Your company will address your needs if they are both defined clearly enough that your manager or other budget decision maker will agree that it's a problem and if your company has the money to do this while being moderately fair. I point out "moderately fair" because if you are working on the same horrible machine as most of your office in a company that is strapped for cash, they may well not be in a position to approve upgrades. Particularly when they can't upgrade one horrible box if they are all horrible.