How to get rid of varicose veins on legs? I want to wear shorts in summer.

See phlebologist. Go to phlebology.Org and seek the help of a qualified phlebologist by placing your zip code on the left side of the home page, and a list of those close to you should be available. Evaluation starts with an ultrasound of the veins in your legs, then applying modern treatment methods of endogenous ablation using radiofrequency or laser, microphlebectomy of vv, and sclerotherapy.
Depends. There are many treatments available and most are done in your doctors office. Depends on your symptoms and severity, simple injection (sclerotherapy), stab phlebectomy, endovascular ablation (radiofrequency or laser) are all helpful - under the right settings. There is not a cure all for all, and more will come (like wrinkles) unless you follow your doctors recommendations.
Seek treatment. As dr. Isobe said, you want to see a phlebologist and discuss the plan that he or she has for treating your veins once your evaluation, including venous ultrasound, has been completed. Get started early though, treatment is a process. It might be too late for shorts this summer but you should be in good shape for next summer.