If a person had a stroke on the left side of the brain, does that usually mean he/she can no longer speak?

Not necessarily. While it is true that the left side of the brain usually houses are "speech centers", not everyone with a stroke on the left side will lose their speech. It really depends on the size of the stroke and the location of the damage. There are strokes that will affect speech production but preserve speech comprehension and others which will do the opposite.
Often. The speech center is on the left side of the brain so a stroke on that side is very likely to affect speech.