I did this last year.. I'd recommend doing some fitness training 2-3 times during the week - so go for a very fast short distance (around 5k is usually good for a busy weeknight I find) run, doing interval training (running at a slow pace for 2 minutes then running fast / sprinting for 30 seconds), fartlek training which is similar but you do more random intervals depending on how you feel (so you may speed up between two lampposts, run up a hill instead of taking the flat route), or something else whether it be swimming, cycling, going to the gym, whatever you enjoy. Just do what you have time for, make sure you're enjoying it or else you won't do it - buy some headphones or something, I can always convince myself to go and listen to an album for a bit and forget I'm being healthy.
Then on a weekend try to do a long run - so if you're working up to a half marathon you may start at 4 miles and work up to being used to running 8-10 miles.
Don't underestimate doing a bit of weight training too. Focus on your legs but generally a whole body workout will help your muscles cope with being put under stress during a race.
Hope you enjoy it!