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Ignore my comment about the giant. I was just trying to think of a metaphor for you. I didn't mean giant, the adjective, but giant, the noun. Your computer is a giant in its power - it's just a small size.

My light brown table supports the intelligent computer system at the opposite side of bed. This sounds like the table is on one side of the bed and the computer is on the other - clearly not right..

If a stool is "lying" it sounds like it's on its side. Just say it's resting or standing.

You do NOT seperate the subject from the verb with a comma.

On the opposite side of the bed, my light brown table supports the intelligent computer system. 

On the opposite side of the bed from WHAT?

HERE IS SOMETHING                  HERE is your bed             Here is your table, on the opposite side of the bed from "Something."

 A   THING X      B

If you are sitting where A is, B is on the opposite side of THING X.

A is on the opposite side of THING X as B.

Okay, the bed it THING X. I totally get that. The computer is A. What is B?

On the opposite side of the bed... from me? Am I just standing there, looking across the bed? If so, then say something like I see my bed, and then, on the opposite side of the bed from where I stand, I see my computer. Does this add anything? If not, there is NO REASON to use the word opposite. Next to my bed. Near my bed. Beside by bed. Not far from my bed. On the opposite side of the room FROM my bed. But if you say something is opposite the bed, you need to say what it is opposite of.

If this doesn't make sense, then I won't try again. Write it however you want.