How to determine optical activity of a compound without asymmetric carbons theoretically?
A substance will be optically active if it is not identical to its mirror image. Check out this great answer to see why. So the dullest and brute-force-est way to find out whether a molecule is chiral is to draw it, to mirror it, and then to attempt to overlay image and mirror image using only rotation. (Remember to draw molecules three-dimensionally!)

But there are a few shortcuts. You can look at the molecule as a whole and check out what symmetry features it has — determine its point group. If a molecule has a centre of symmetry (i.e. inversion results in the identical molecule), a plane of symmetry or improper rotation (which is a rotation followed by mirroring along a plane orthogonal to the rotation axis) it is achiral. If you cannot find any of these symmetry elements, the molecule is chiral.