What tools would I need to have/borrow/buy to build a table?
It depends in no small part on how you wish to construct the table.  For instance, if you wish to do a simple screw or nail construction, it's a different set of end tools than if you wanted to do dove-tail joints, or biscuit joints, or mortice and tenant joints...

The basics (screw construction)


Measuring tape
Pencils 
A straight edge (usually part of a related
tool) 
A saw 
A drill (for pre drilling screw holes) 
A screwdriver or driver bit for your drill - for installing the screws 
Several grits of sand paper from coarse (60 grit) to ultra fine (220 grit) 
A sanding block (flat surface used to keep your sand paper flat)