You have to believe that there is only one God, Allah, who created the
entire universe, and that Muhammad (peace be upon him) is his final
messenger on earth.
If you recite this, with total sincerity, in front of two witnesses,
you have become a Muslim. It really is as simple as that.
Muslims call this recitation the Shahada, and refer to it as the first
Pillar of Islam.
And if you become a Muslim by converting (some Muslims would say
"reverting") to Islam your fellow Muslims will accept you as if you had
been born a Muslim.