I want to start strength training. Advice needed

You're really smart to think about adding strength training into your fitness routine. I really like Fitness Blender (.com). I'm getting ready to do one of their free videos right now. The creators, a couple Kelly and Daniel, really promote strength training as a component of your exercise routine. I finally got a nice set of dumbbells last xmas, but before that I did their body weight only strength training videos (or used my 5 lb weights). I've been (more or less) maintaining my weight with them for about three years now (I also do their HIIT videos). They are smart, motivational, and have a ton of free videos to choose from. Anything from 5 minutes to 90 minutes. These videos are a great option if you can motivate yourself to workout at home. Good luck!! I think you'll need to give yourself about 3 - 5 weeks of consistent strength training before you'll really see the results. I'm starting over from a couple months of doing nothing, so I know how hard those first few weeks can be. Stick with it!!

Have a look at the Starting Strength channel on YouTube.It's all about beginning weightlifting.They also have a book out.
There are a number of good lifters on YouTube.Alan Thrall,Megsquats,Athlene-X.
I've been lifting for ages so I do enjoy watching good lifters.But I can hardly remember starting.It must have been learning from magazines back then.

As far as books go, I'd recommend Strong Curves (Bret Contreras) and Starting Strength (Mark Rippetoe). New Rules of Lifting seems like another good one, but I admit I only flipped through it at the book store. Wendler 5/3/1 is a good book, but I wouldn't really recommend the program to a beginner. If you're training at home, You Are Your Own Gym would be worth a look too.

For those recommending 5x5 SL and Starting Strength note that OP works out at home and has access to dumbbells/free weights (which is unlikely to mean an Olympic bar, stands, and bench that is required for these programs).

I would recommend a site called aworkoutroutine.com

It is comprehensive in explaining everything about lifting routines and even includes a very good beginner routine for free. He also has a book of several workout routines that I would also recommend.

Just to give a basic idea of what you can do at home.Dumbbells,or other simple weights can be used.You could do squats with a 20-30lb pound of sand,or cat litter.
The most basic split will be Legs,The upper body Pushing Muscles,The upper body Pulling Muscles.
You can do the whole upper body in one day if you don't have the time for three days a week.
Otherwise you can do Legs/Push/Pull three days on one off,or one day on one off.Whatever works for your schedule.
Start with a warm up to get your blood going.Walk around,shadow box.Just get moving.
Start with compound movements.That means multiple joint exercises.Hips,and knees.Shoulders,and elbows.

Legs-Squats unweighted,squats with dumbbells,Lunges,Step-ups on a step block,calves raises.
Push - Push ups,against a wall,or from your knees if you're not strong enough to do full push ups.Dumbbell presses from the floor,shoulder presses,triceps extensions.
Pull-Dumbbell rows,bicep curls,forearm curls.You can do abs on this day too.Sit-ups or leg lifts.

The more equipment you have the more you can do.A bench helps.A barbell.You can do a lot at home.
I started using home equipment when I was pretty young.I did go to a gym for awhile.But it's so convenient to have a home gym.I have a power rack,and pulley system.Bars.Dumbbells.Plates.And of course a plate tree,and dumbbell rack.I've just added to it over the years.
Weight training is not really intimidating.Some people just like to make it look that way.The idea of resistance training is as straight forward as it gets.And it's tremendously adaptable to the individual.

This was so helpful to me when I was getting started and working out at home with dumbbells: http://community.myfitnesspal.com/en/discussion/902569/barbell-routines-when-you-only-have-dumbbells/p1 Eventually I joined a gym and switched to barbell, but you can go a long way with dumbbells and don't ever need to switch if you don't want to.