We tend to use software called "Target". This is mainly a compatibility issue; we have it, we use it, we get good at it, so others use it, etc. We certainly don't pretend it's the best software in the world, but it's quite cheap, there is a free student version available, and there is a lot of local expertise (and libraries of components).
Don't expect Target to do anything except schematic-capture and layout. Though the software can do electrical simulations and physical 3D modelling, we almost never have the circuit or physical models required for the components we use. Anyone got a SPICE model for a microcontroller?!!
Our version of Target lets us design up to 4-layer boards with unlimited nodes. The student version is more limited.
There are lots of other PCB layout programs, but decent ones tend to be expensive. There is an open-source program call KiCAD which is growing in popularity, and has a very large user base and support, so that may well be worth considering in future. However our local expertise with Target counts for a lot.
All PCB layout software produces "Gerber" files, which are just pictures of the layout for each of the layers that make up a PCB. Once you have those, you have to consider how to actually make the thing.
