One becomes a muslim by believing in Allah as the only one worthy of worship, and believing that Prophet Muhammad (pbuh), was the last and final messenger of Allah.
For anyone thinking about becoming a muslim, really this is the only thing required of them as the first step. Believing and affirming the aforementioned beliefs takes one in to the fold of Islam.
Of course one can gradually, learn and practice all the ahkam. or rulings of Islam. Like praying, fasting, or covering up for women....this can happen slowly, with help from fellow muslim brothers and sisters. But the most important thing is to say the following:
Ash hadu Allah Ilaha Illallah wa ash hadu anna muhammadan abdu hu wa rasuluhu.
The translation of which is:
I bear witness that there is no God worthy of worship except Allah and I bear witness that prophet Muhammad (pbuh) was the slave and messenger of Allah.
One is officially a muslim after saying and believing the above words. Someone who has accepted Islam is forgiven all his past sins, and his record of deeds is started afresh. He is again just like a new born baby, and is in a state, where Allah accepts all his duas (prayers). Please pray for me too, inshallah.