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(Admittedly sparse) Section on Historical Muhammad
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As /u/someguyupnorth said, it is pretty hard to establish the historicity of anyone without any doubt at all, all the more so in antiquity/early middle ages as sources are so scarce. Having said that, the Western scholarly consensus is that Muhammad did exist and that the basics of his life is largely accurate, though the specifics are still argued over, such as over what kind of movement he led.
There are two possible early mentions of Muhammad and his movement. The first is an anti-Jewish pamphlet (supposedly) written in Africa in 634, which claimed that some Jews were convinced by the rise of a new unnamed prophet amongst the Saracens (Arabs) as a portent of a new Messiah. The second is a short note written on a Syriac Gospel book around 636, presumably written by a monk writing down the momentous events he just experienced - the most important line being:
... many villages were ruined with killing by [the Arabs of] Muhammad and a great number of people were killed and captives [were taken] from Galilee as far as Beth
This note however is faded and the reading uncertain, so Robert Hoyland, a historian who basically wrote a book covering all the sources for early Islam, prefers a chronicler's account written around 640 as the 'first' mention of Muhammad, which said that:
In the year 945, indiction 7, on Friday 4 February (634) at the ninth hour, there was a battle between the Romans and the Arabs of Muhammad
These sources don't tell us much, but clearly someone called Muhammad existed and was a very important figure for Arabs invading Palestine in the 630s. It would be very unlikely for someone who didn't exist to be important enough to be recorded by their enemies! Note that I'm excluding Islamic sources from this discussion, as they were all compiled at least 150 years after Muhammad's death and are considered by some historians to be not very useful sources for early Islam. The Quran however was written around that time, so a religious system was being developed. As the sources I quoted above all mentioned that Muhammad was a leader of some sort (the pamphlet even called him a false prophet), when looked at alongside the vague mentions of Muhammad within the Quran, there really is no reason not to see Muhammad as a historical figure who was both a successful political leader and a religious reformer.