Can someone help me in understanding the suffix
I am not able to understand it properly and I always mix the spelling like:
- "computor" when it should be computer
- "administrater" when it should be administrator
As reflected in comments, there's no real "rule" here (though there's a tendency for -or to occur more often in words with Latin roots). So basically, you just have to learn them.
But things aren't as bad as they appear. Not only is the -er form more common in established words - it's far more "productive" for new terms. Also, as RegDwight points out in this ELU answer on the subject, there are many words where either spelling is acceptable (adviser/advisor, convener/convenor, etc.).
So instead of having to learn every word separately, all you have to do is remember those where only -or is acceptable (which as of today, includes administrator).
In short, slow as it might be, the general trend is towards -er. Adopt that as your default, and with any luck by the time you need one of today's more obscure "-or - only" words, the -er form will be acceptable!
EDIT: As @Anixx correctly points out, strictly speaking there is no currently productive suffix -ter in Modern English (the only instances where it's recognized as a meaningful "morphemic element" are laughter::laugh and slaughter::slay). This question and answer address the -or / -er distinction.
There is no suffix -ter- in English.
If the 't' is part of the root, then English uses the suffix -er. If 't' is not a part of the root, then English uses Latin suffix -tor-.
Note that the suffixes have different origin. The suffix -er also was borrowed from Latin but from Latin suffix -ari- (-arius with the ending).
There are also English words with suffix -ster as in hipster, youngster. It was initially a feminine suffix. They should not be confused with the first two.
There are also some words inherited from PIE which had the -ter- suffix in PIE but in English it became a part of the root ("daughter" for instance).
There is also a usage trend to use -tor when the intent is to emphasize that the agent is a person, while -ter is used when the agent is not necessarily a person.
For example, ‘computor’ the original term meaning a person performing computation later becoming ‘computer’ when calculations were performed by either people or machines. Following a transition period where either word was used for either meaning; computer is now commonly understood to mean a machine.