It's all pretty well documented actually. Yes - Ancient Egyptians did build the pyramids in Egypt. This isn't a matter of belief or speculation, there are more than enough facts to corroborate when, how and why the pyramids at Giza were built.
Here is the logical progression of how pyramids came to be in Egypt:
1) Mastabas. These are basically large slabs of rock that you cover the mummy with to keep animals away and also to mark the grave.
2) ~2600 BC Imhotep comes along and decides to build a step pyramid by stacking increasingly smaller mastabas on top of each other for the pharaoh Djoser (this was the first stone building in the history of the world by the way).
3) ~2500 BC The pharaoh Snefru gets the idea to start building "true" pyramids by filling in step pyramids with limestone on the steps. The first few of them collapsed (Bent Pyramid, Meidum Pyramid) or were abandoned but he eventually gets it right (Red Pyramid).
4) Snefru's son Khufu had the first Pyramid at Giza built using the knowledge he got from his father.
The interesting thing is even the Ancient Egyptians forgot how to properly build pyramids - that's how long they reigned for. (
http://en.wikipedia.org/wiki/List_of_Egyptian_pyramids) that page shows images in chronological order of the existing know Egyptian pyramids. You can see how they learned and then forgot over time (over the course of 1400 years).
Also - there's no evidence to suggest a significant amount of slave labor was used to build the pyramids - there weren't even that many slaves in Egypt during that period. Egyptians were expected to spend a certain amount of their time doing civic work. It would be like one day a week you had to put in work for the community or Egypt as a whole. Rich people could pay someone else to take their place and also it could be argued that this is "slave" labor - but in reality it wasn't - it was just how their society worked.
ps - this civic work would most likely be done during the season called "Inundation" which was about 4 months when the nile was flooded so there wasn't much else for the farmers to do and it would also be a lot easier to float limestone directly to the building site.