Learn Swedish: Kanalen sänder dokumentären klockan tio över fyra. - The channel broadcasts the documentary at ten past four.

In Swedish, you generally don't use a preposition like "at" when stating a specific time. The word klockan (literally "the clock") does that job for you. So, to say "at ten past four", you just say klockan tio över fyra.

Does the verb sänder just mean "to send"?

Yes, att sända is a cognate of the English "to send" and can be used for sending items, but it is also the standard Swedish word for broadcasting or transmitting a TV or radio program.

If över means "past" the hour, how would I say "ten to four"?

To express minutes leading up to the next hour, you use the preposition i (in). So, "ten to four" would be tio i fyra.

How would the sentence change if I started it with the time instead?

Because of the V2 rule in Swedish, the verb must always be the second block of information in a statement. If you put the time first, the verb sänder and the subject kanalen must swap places. It becomes: Klockan tio över fyra sänder kanalen dokumentären.