Short answer - Yes you can remove a light fixture and put in a ceiling fan. The fan motor and fan light would be wired together and each controlled individually from a pull chain. Power to the fan is controlled from the wall switch. Typically the fan LIGHT stays on, the fan MOTOR stays off and the entire fan becomes a light fixture controlled from the wall switch. That way when you enter a dark room you can easily turn on the light from the wall switch.
Long answer, the elec. box that the fan mounts to, must be rated for the weight of a ceiling fan so it won't pull the elec. box out of the ceiling. If the current light fixture is a chandelier (weight) then elec. box might be ok. If you have attic access you can find the box and check it. Look online to see the difference between a elec. box rated for a ceiling fan vs a light fixture. You can also cut a bigger hole around elec. box to check or replace it, then patch the enlarged part of the hole with sheetrock and use a "ceiling fan medallion" to make it pretty.
The elec. box would be the biggest challenge, the fax installation would be the easy part. If you had to cut sheetrock, make sure patched sheetrock is sealed around the elec. box with chalking so that you don't lose conditioned air to the attic.
If you are unsure about it or if deed restrictions require a licensed electrician then don't do it. A licensed electrician would be cost prohibitive for most people.
