I am changing out two adjacent light switches and came across a wiring
challenge that I'm hoping someone can help me with. Please forgive me
in advance for my lack of proper terminology...

The first switch is connected at the top screw to a black wire, and at
the bottom screw to an older wire with brown cloth insulation.

The second switch is connected at the top and the bottom to the same
type of brown-cloth insulated wires. However, at the bottom screw,
there are two wires attached to the one screw, one of which is the same
wire attached to the bottom screw of the first switch (?!).

This can't be good, right? Can I fix this on my own, or is it time to
call in an electrician?

Many thanks for your help!

Kimberly