There are many places in most communities to learn social dancing. If you are determined to learn modern dancing NOW, take private lessons, and be prepared to have those lessons continue for more than a year. Dance is often a body contact activity. You need not overdress. Ties are not essential dress for men at most dance venues, but a clean shirt is.
Running shoes are no better.
They might be comfortable to wear, but they grip the floor too much for dancing. You need a shoe with a leather sole that is firm on the floor, but will also slide. If you can, keep one pair of shoes that you only use for dancing. Never wear those shoes on the street. Women are happy to dance with even the worst dancer who shares his bad dancing around.