There are three different types of rest areas for different situations. Separate bunks like this are a class 1 rest area.

A class 2 rest area is a standard lie flat first/business class seat seen in most long haul international flights. In this situation, a specific seat is designated as crew rest and would have a privacy curtain that separates it from the rest of the cabin. This seat would be sold as normal on a flight where crew rest is not required; however, the passenger would not be allowed to utilize the curtain.

A class 3 rest area is usually just a row of coach seats with more recline and foot rests, typically the last row or two. Most of these that I have seen also have a privacy curtain that can be put around the seats.

There is usually a small placard to indicate that it is a crew rest seat, and what type of crew rest it is.

I believe in all instances the crew are entitled to sit by themselves and not directly next to anyone, so if the first class seats are in a 2-2 configuration, they would have to block off both seats on one side for one crew member.

All of this can play a big part when deciding what planes to send where.

For a short time I was tasked with finding planes with crew rests out of service and blocking off first class seats for the crew to use instead. Some crew like the first class lie flat seat better than the bunk (a little more room, TV) and would write up erroneous maintenance items for the bunk so that they would get the first class seat.

Edit: most of this knowledge came from my experience at one of the big three. Various unions have various contracts which may require different rest rules.