In terms of sources of leaks - what are the main culplrits?
There's a few weak spots that I always check. The first in the corners - where the tiled walls are intersecting. Another weak spot is where the tiles meet the floor. And a third weak spot is the tile grout. Grout can crack but it's also porous. Customers are often surprised to find out that grout isn't waterproof, it's only water resistant. This is especially in the case of a cheap grouts used in conjunction with a power shower.
What are the first signs of a leak?
An early sign can be light spotting like tea stains on the ceiling of the room below. In the case of a bigger leak, people may see water is coming through a light fixture in the room below or just dripping from the ceiling. If the problem is very advanced, the plaster board behind the tiles will get damp and bulge, causing the tiles to start cracking or lifting off the wall. In the case of a downstairs link, customers may seem water on the floor or floor boards starting to bulge and lift.
What's the first thing someone should do if they think they have a leak?
Get someone into look at it as soon as you can. Of course, you should stop using the shower or bathroom until you know what's happening.
What's the solution?
The only way to really fix the solution and have peace of mind that it's not going to happen again is to redo the whole area correctly. That means removing the tiling, replacing the plaster board, tanking (waterproofing) the area correctly and sealing and regrouting the area with high quality products. I like to use a German range called Botament. It has higher concentration of silica than cheaper grouts so it's more flexible and durable.
Silicon may work as a temporary fix but sooner or later the weight of someone standing in the shower tray will cause the tray to flex and may break the seal. That's not a problem if your shower or bath is tanked.