To pick or “click” on a geometry items, you need to cast a ray (line-segment) out from the camera and then test against every triangle in the scene.
This can be very expensive depending on the amount of geo / tries in a scene. To get around this there is a tree structure called an OctTree which is used to query regions in space.
I would suggest looking into projection from screen space into world space, this will help with the creation of a line segment from camera into the world. Then loop over every bounding box if you have a bounding box for your geo. Check if line segment intersect AABB. If it does intersect then loop over every triangle in the bounding box and use the line intersect with triangle formula, and see if any triangle returns true. As soon as you have a true break out of the loop and SUCCESS you have hit the geo.
Math centric write up : geometry - Determine if a line segment passes "through" a triangle ... - Mathematics Stack Exchange
Palatable answer: c++ - How to know IF a line segment intersects a triangle in 3d space? - Stack Overflow
I hope that helps