If you want to be a faster and less injury prone runner then strength training needs to get done. I don't actually like weight lifting very much but due to so previous joint damage and also because I like running fast and I really hate being injured. I wish just running was enough to stay strong enough to run well but there are a whole bunch of studies showing that's just not the case, especially as the years roll by. I have done strength training pretty regularly a lot longer than I've been a distance runner and am reasonably knowledgeable so I decided I could probably find a way to get my whole body strength trained every week without having to spend too much time. Before I explain what I do, let me remind you that improper form with some lifts can damage you. Badly. If you aren't sure then get someone to teach you.
In order get some cardiovascular benefit from my strength training I use a rhythm of work and rest called 'tabata', which is 20 seconds of work then 10 seconds of rest repeating for a minimum of four minutes though I prefer five minutes. Tabata is shown to give cardiovascular benefits. I have a timer called a Gym Boss that can be programmed for any interval length and is great for all kinds of workouts. There is a downloadable ap for tabata as well. I bought it online for 20 bucks. Since 10 seconds isn't enough rest to allow a solid effort on the next set what I do is alternate between to different lifts so that I have 50 seconds total to recover from a given lift. Here is a list of all the lifts I do, though once in a while I vary the exact lift, for example a flat bench fly instead of a press. If you aren't familiar with the weight lifting terms take yourself over to you tube. I spread this across four days because the equipment is in my basement but one could break this into just one or two days
Flat bench fly and Seated row (though any row will work)
Flat bench dumbell press and Wide grip pull down
Five minutes rotating through ab exercises
Squats and Arnold Press (or military press with dumbells)
Incline dumbell fly and reverse fly (which can be done on the incline bench)
Single leg extensions (its rehab for a knee and otherwise I'd do single leg dumbell squats)
Alternate legs instead of changing exercises
Incline bench bicep curls and Rope Tricep push downs (I alternate arms for the curls)
Wide grip curls with a bar and Skull crushers (or close press)
Five minutes of rotating ab exercises
Deadlifts and Dumbell side raises
Decline bench dumbell press and Upright row
Single leg deadlift with a dumbell (hold the dumbell in one hand and stand on the OTHER leg and alternate legs)
The ab exercises I do; 1. hanging abstrap curls which I usually do as side curls for the obliques and for improved lateral stability. 2. ab wheel 3. butt lifts where you lie on your back with your feet straight up and lift your butt up.
Why so many dumbells? Machines are bad news. Unless you are an average size and frame man the machine isn't really made for you. Additionally, with dumbells your body engages stabilizers more than with bars or machines. If you're planning to run around in the woods stability is good. Sure you can't lift quite as heavy with dumbells so you won't gain so much muscle mass....oh wait, I'm a distance runner. What about these awkward single leg lifts? They improve your balance. They even out your strength. Many, many injuries and chronic running pains are mostly the result of strength imbalances. Don't skip body parts just because you don't like the lift. The single leg deadlifts in particular are something that has helped me handle hilly technical trail faster which is a whole lot of fun.
How do I decide how much weight to use? Well, start 5-10 pounds lighter than what you think is a good idea since its better to go a little light than get hurt just cross training. After that whatever you can do for five sets. I vary my weight and pace from time to time. How many reps is a good goal? Well, that varies with the lift too. There are things like dead lift that I always do slowly with extra attention to form so I don't injure my back again (snowboarding). I get seven or eight reps into twenty seconds. With something like bicep curls I go a little faster. I never, ever straighten my elbows or knees all the the way. I don't lift in the seven days before an ultra distance race. I don't lift on days when I do speed work, hill repeats or long run day. I do lift on the two days a week when I don't run which makes me more comfortable taking the days off from running.