It sounds like you already know how to find JPs (perform a gravitational survey with a ship that has grav sensors). To jump, you need either a jump drive or a jump gate.
You research jump gate construction modules (Construction/Production category), put one on a ship, then order it to build a gate at the JP. Gates are one-way, so you'll have to build both sides separately if you want a two-way gate. Gates are permanent and indestructible, and all ships can use them (even without a jump drive).
FYI civilian traffic requires gates, not drives. By civilian I mean the shipping line-controlled freighters/colony ships. Your own commercial ships can use jump drives.
Also, if you don't already know, here's how commercial and military jump drives work: Commercial drives can only transport ships with commercial engines. Military drives can only transport ships with non-commercial (i.e. military, gunboat, and fighter) engines. It doesn't matter whether the ship is commercial or military. Only the engine and jump drive matter.
There are a few other ways to find JPs: witness another empire's ship passing through one, or learn about them through diplomacy/conquest.
There are also several ways to use jump drives, each with varying rules.
- Standard Transit
- A jump-capable ship cannot transport a ship larger than itself.
- If you park a jump-capable ship at a JP, other task groups can perform a standard transit from either side of the JP.
- A jump ship can only transport ships with engines that match its drive (commercial or military). I don't know how a jump ship with both COM and MIL jump drives works.
- Squadron Transit
- Size and drive/engine compatibility work the same as for standard transit.
- The task group cannot contain more ships than the jump drive can handle. I don't know which jump drive is picked should there be more than one jump ship. I'm also pretty sure ships/fighters inside a carrier don't count against the limit.
- The task group will exit the JP at a fixed distance (depends on the drive) in a random direction. As you can imagine, this makes it very useful for jump point assaults or recon in unknown or dangerous systems.