Start small. Get yourself the course/syllabus materials for the Cisco ICND1 and ICND2 (CCENT and CCNA R&S). From there you need to decide if you want to diversify into a particular networking field (Wifi, Voice, Design, Security, etc) or if you are going to stay with the "Core" Routing and Switching track.
Experience is typically held in as high (or higher) regard than qualifications, so you'll need to work your way up the career ladder also. Get yourself in at the bottom as a network tech/engineer, preferably at a Cisco partner or at least a business that utilizes a majority of Cisco equipment.
Getting hands on is most definitely key, which is why a lot of "pupils" of Cisco tracks end up owning their own lab kit (I do, plus run my home network on Cisco kit), but don't go all in immediately, the earlier qualifications can be studied for using software (GNS3, Cisco Packet Tracer), but a few cheap and simple physical devices wouldn't go amiss for giving yourself opportunity to do the few things you can't do in emulators and simulators (physically configuring, firmware updates, password recovery, etc).
As for timescales, well really putting your spare time into ICND1 and 2 should be possible within 3-4 months in reality (I did it in 2 I seem to recall).
