They were an upstart clan that battled against the Ottomans, had their assess haded to them on a sliver plate, relocated to Nejd, teamed up with the Muslim equivalent of fundamentalist American Evangelical preacher, went to battle against the Ottomans again, won and established their rule over Nejd and Hejaz.

The British didn't care so long as their interests in India were not threatened and so the British didn't interfere until the Al-Saud started to attack the smaller emirates (Kuwait, Qatar, Bahrain, future UAE) and even then only to have their ships flex their muscles to scare off the Saudi forces.

This is a very rough, and dumbed down history of the rise of the Al-Saud dynasty.