Walls and Ceilings - Stud Damage

While repairing some water damage around the shower, I found out where the ants in my house are coming from. They seemed to have put up shop in my shower wall. They also did some damage to one of the studs supporting the window frame and it looks like they went clear through.

Is it necessary to fix this, and how does one go about replacing or adding a new stud? I haven't been able to find any info about this on this or any other site.

Yes, you should remove all water and insect damaged wood now while the wall is open. There are several ways to replace the studs. If the damage is limited to the bottom, cut off the bottom and nail a new stud next to it. If you need to replace the entire stud, you can place a new one on either side and then cut out the damaged one. You have to play it by ear depending on the actual situation and extent of damage.

You just cut it to length and hammer it into place and nail it?

Yep. The only studs to worry about (that is, require more planning and support) are the ones supporting the ends of a header.