It can take as little as a couple of days--most of the tools even let you draw simple logic schematics. But this is useful only if you have something that fits the use cases for FPGAs.
The problem with FPGAs is that they're only really useful in very narrow niche applications--generally with hard real-time constraints. So ... motor controllers, high-speed ADC/DAC interfacing (think software defined radio), weird processing algorithms that don't work well on a DSP, safety interlocks, etc.
Most people are far better off learning a microcontroller family in depth (think: STMF32 series, for example). You can really bend the functional units of a microcontroller a long way from their intended usages in order to abuse them to do what you need under most circumstances.
I don't reach for FPGAs much anymore as an embedded engineer. Normally I trawl through the various microcontrollers to see if I can make something do what I need. If those don't work, the next layer is to look at SoCs like the AM3359 from the BeagleBone Series which have stronger processors to run Linux (Linux provides larger storage, CPU, and lots more communication options) but have hard real-time units (the PRUs).
Finally, if even those don't work, then I'll start thinking about a cheap FPGA in concert with an external microcontroller.
One unusual thing is that I'm an absolute bigot about not putting microcontrollers inside my FPGA (neither soft nor hard cores). Even the worst microcontroller toolchain is better than the best FPGA toolchain so I am adamant about external microcontrollers.