I started around 24, realizing that if I was the same weight then that I was when I graduated high school, things weren't going to change without effort. I had no idea what I was doing at first, as before then I only ever went to a gym because that's where the volleyball court was, or the tennis court, or whatever. I actually went with an online personal trainer at first, as it was much cheaper than an in-person one and I figured I was self-motivated enough to get myself to the gym even if there was no one to chew me out if I didn't. (I used www.plusoneactive.com
, which allowed me to tell the trainer what I was looking for, what level of time I was willing to commit, and where I could leave feedback about difficulty and ask questions and have him answer them and adjust my workouts accordingly within a day). These days, you can find good videos of how to do most exercises at sites like RealJock, so it's not as important to hire someone to tell you how to do a given exercise, but it could still help in designing a routine.
I started out with 3 times a week, half an hour at a time...which turned in 45 minutes...which then eventually saw me moving to 4 days a week..and so on. I felt that it was important to start small and slow, and just make it such an ingrained part of my day that I didn't even question whether I would be going to the gym.
It took me between 3 and 6 months to notice real-life strength changes--carrying my groceries home became easier, my pulse changed less from climbing 3 flights of stairs than it had before, rearranging the furniture was suddenly not a big deal to do, etc. It took more like 6-9 months for me to see significant visible changes, though my (platonic) roommate at the time commented on them before I could see them myself. As a caveat, though, I was coming from the direction of the way too skinny trying to make it into healthier weight ranges; that can take some people longer than the opposite direction, but of course it varies from person to person.