Simply by saying with conviction, "La ilaha illa Allah, Muhammadurrasoolu- llah" one coverts to islam and becomes a muslim. This saying means 'There's no true god but God(Allah), and Muhammad is the messenger of God' The 1st part, there's no true god but God means that none has the right to be worshipped but God alone, and that God has neither partner nor son. To be a muslim, one should also:
#Believ that the holy Qur'an is the literal word of God, revealed by Him.
#belive that the day of judgement is true and will come, as God promised in the Qur'an
#Accept islam as his or her religion.
#Not worship anything nor anyone except God