Recently I've been jogging and working my arms with some exercises. Although I feel both legs and arms more or less equally tired I also feel I have much more strength with my leg and right arm. I also feel that the right side of my abs are more tired (one or two days after the exercise), besides this I can see that my right shoes are more worn... so I was worried about this. Now that I'm starting to do more exercise I would like to have both sides of my body more or less equally developed. What should I do? Should I try to put more effort in my left side consciously?
First of all, given we don't know much about the exact situation - have in mind there could be an underlying medical condition so you should consult a doctor if you have any such doubt.
That being said - having more strength on your right side, especially in the beginning is not unlikely. Your strength is not solely determined by your muscle shape and size but how well your nervous system knows how to coordinate your muscle tissue to produce work (muscle unit recruitment). Actually when a person starts weightlifting for first time, there are massive strength gains first few months mostly because of improved muscle unit recruitment. Given that through your life you have used your right hand for many demanding tasks, or have your right leg stepping first when climbing stairs etc, there could be such natural imbalance. It's significance should decrease over time.
A tactic strength athletes (especially bodybuilders) apply to have equal development is doing unilateral exercises at the end of their workout. Eg one hand biceps curls or altering leg lunges - doing equal number of reps on either limb. But have in mind that you should focus on big movements and full-body workouts in the beginning (squats, deadlifts, vertical and horizontal pushing/pulling), not using isolating exercises. Those basic exercises will work your abs much better than crunches. You might however include isolating (single joint) exercises at the end of your workout to help you feel more confident that you are equating the development of your sides.
Ditch the cables and machines and pick up a barbell. Squat, press, bench and deadlift should suffice in developing your whole body. These big compound movements (if used with good form) should help your body account for imbalance.
Unilateral: For example, my left arm is weak so I do a set to failure of bicep curls on my left arm first, counting the reps. I then repeat that number of reps on my right arm, no more, no less.
DO NOT ONLY EXERCISE ONE SIDE OF YOUR BODY
If you're seeing uneven wear, it is worthwhile seeing a doctor. It's not out of the question for there to be a fundamental unevenness. I had a mild case of undiagnosed scoliosis as a child and, possibly as a result, my arms are slightly different lengths, which means I have to modify my bench-press and push-up motions slightly. I do not advise seeing a chiropractor as my experience with them, and from seeing others with them, is that they will diagnose a spinal imbalance and "vertical subluxations" no matter what your condition and will immediately try to push you for weekly woo sessions.
As with JJosaur's advice, do some more whole-body exercises. Don't worry too much about working one side or the other. If you work them equally, things will likely even out. I do applaud you for wanting to be balanced.