It is possible to do both but most people don't know what they're doing enough to gain muscle and lose fat at the same time. Anyways, what you want to do is start lifting five days a week. Each day pick one of the muscle groups from the list below, so that you end up doing a total body workout by the end of the week.
chest
back
arms (biceps and triceps)
legs
shoulders
You can pretty much do abs 2x a week on any day you feel like it. You'll want to do a lot of free-weights, and it is very important that you do the exercises properly. Remember the Tortoise and the Hare? Keep that in mind when you want to start working out. Don't try to achieve more results than possible with zeal in the beginning, just follow the plan and you'll see results after 2 months. After 6 months you wont look the same, after a year you will be a new man. Anything faster wont last, and wont be real.
So do about 4-5 exercises for each of the muscle groups (for arms do 3 bicep, and 3 tricep, that's the longest workout day of the week with this plan).
How much should you lift, and how many reps? Well the most important thing is to do reps until failure. I used to do pyramid type workouts, where you start with a warm-up set, about 13 reps, 1st set, pick a weight that you can lift 10-12 times, and can just do last rep without needing help. 2nd about 10lbs more, set a weight that you can do about 8 reps with, 3rd set you add another 10lbs or whatever so that you can only do 4-6 reps, for 4th and 5th set go backwards to the weights and reps you did for 2nd and 1st sets.
Next, your efforts will be useless without proper diet. Eat a lot of protein. Eat breakfast, eat lunch, and eat a balanced dinner (I never eat too much pasta or anything carby, but I also don't go out of my way by throwing out the buns for my burgers, I'll eat a burger, and then hav ea second patty without the bun to get my extra protein). You can only digest about 30 grams of protein in a sitting, so you will have to eat every 2 hours, a small snack, like hot dogs, tuna, chicken, fish, etc. If you work out properly you will always be hungry, so plan ahead to have something available to eat every 2-3 hours.
Make sure you get proper amounts of sleep too.
Next, you will want to do cardio 3-4 times a week. Best time to do it is first thing in the morning, before breakfast. 1 mile? Not enough. Run for at least 20 minutes. For the first couple months you will have to push yourself each time you run, always go at least the distance you did last time, and try to push for a block or two or three or four more each time. After a month you'll get up to around 45 minutes, it's extremelly boring, and by that point you will want to stop your runs as a result of boredom rather than not being able to continue.