Your 3d object is a bunch of vertices, right?

And those vertices have a position, right?

The easiest thing is to build a so-called "Axis-Aligned Bounding Box" (AABB for short).

You should be very capable of figuring out how to create such an AABB from your set of vertices.

As for checking for collision between two AABBs, there are two possible ways:

The easiest is to just check two AABBs statically whether they intersect or not.

That is, given two AABBs, specifically their current position, check whether they intersect.

You could simply google for "AABB intersection test" and you'll find numerous examples and explanations.

The next more sophisticated way is to assume that the two AABBs move in a game between two successive intersection checks. When they move fast enough, they could intersect in between two frames and not intersect at the checks at each frame. To remedy this, there is another algorithm which you can google for with "swept AABB collision".