Check the silicon for cream or white areas, and for air bubbles in the silicon. These areas are where the silicon is breaking down and coming away from the glass.
Press the silicon with your finger and see if it is soft and squishy or hard and brittle. Good silicon will be soft but firm. When you press it you will be able to make a small dent in it but it should pop back up as soon as you move your finger away.
If the silicon is hard and doesn't depress, then it is old and drying out. As long as the hard silicon is clear and doesn't have cream/ white areas or bubbles, it should be fine.
If there are no cream/ white areas and no bubbles between the glass, then just use a single sided razorblade to trim the old silicon out of the corners. Do not cut it out from between the glass if it looks good. Just remove it from the exposed areas in the tank.
After you have removed the old silicon, wipe the area with a paper towel or cloth that has some alcohol on it and then wipe it down with some water on a towel. Let it dry and then use some aquarium/ glass silicon to go over the seams where the glass joins.
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*NB* When you use silicon, try to do it outside or have the doors and windows open and a fan blowing.
*NB* Do not put your head in the tank when using silicon because the fumes can cause you to pass out.
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