I'm no expert, but for me it's just been a long progression. Every year as I got more serious, I'd do more mileage. If you're at about 15, then you definitely want to take it slow.
Maybe add 3-5 miles a week for 3 weeks, then do a "regression week" where you drop your mileage down a little bit to keep you feeling fresh and recovered. If you were doing 30mpw then maybe only do 20 for your regression week. If you were doing 60mpw, maybe only do 45-50mpw for your regression week.
The regression week every 3 weeks isn't a set in stone number. If you're feeling run down and tired two weeks in then back it off (a little bit) for one week. Also, don't drastically increase your mileage week after week. Lets say you just did 30 mpw and you're feeling great. So you decide to keep on going up and you do 35-40mpw...and then you get injured. Always stay on the cautious side of things.
As for workouts, focus on slowly increasing your mileage first. Once you think you're at a decent number, you can start working out. One of the most basic, and in my opinion best workouts for getting fast quick is tempo runs. Basically a "comfortably hard" pace. There's no exact number pace for these. I run 5ks in the mid to high 16 minute range currently, and I do my tempos at about 5:45-6:10 pace, just depending how I'm feeling. These are generally for 3-6 miles in distance. If you're new, though, then you can start out by doing "tempo intervals", where you just run at tempo pace for a set distance. Maybe start out at a mile, with a short 1-2 minute jogging break, and repeat.
If you just broke 40 for a 10k then i'd guess your tempo pace is in the high 6 minute range.
As for recovery; Just do your easy runs slow if you're tired. If you're really feeling crappy or sore, take a day off, but try not to make a habit out of it if you really want to get better. I use a foam roller after my runs a few times a week, I think it helps tremendously. Also, if you have a really hard or long effort, taking an ice bath directly afterwords does wonders.