I new GFI was installed in my kitchen by the owner. Now, every time I switch on the garbage disposal, ALL the outlets in the kitchne are tripped off.
What would cause this, and how is it remedied?

Either something is wired incorrectly, or the disposal has a ground fault, which I would expect since is carries water.

The disposal does not need to be GFI protected. Disconnecting it from the GFI may help.

If you described how this is all connected perhaps we can help with that.

It sounds like the former owner (Landlord?)used the load side of the GFCI to run the outlets so, the problem could be the Disposal or an outlet. If it is a LL situation, have them figure out what is wrong. If not, and it is your house, turn off the breaker to the GFCI, pull the GFCI out, disconnect the load side wires, black and white, reset the breaker and GFCI and try the Disposal. If it works, you have a problem in the outlets. If the GF trips, you have a problem with the disposal.

GFCI is the only new factor here. It is replacing what was formerly a regular outlet. Common sense tells me it's the way it was wired. What's the correct configuration on the GFCI?

How was the old outlet wired? I suspect that power was taken to the old outlet, which was a split outlet and then to the other outlets in the kitchen. Switch leg was wired to the switch and then back to the other half of the split outlet for the disposal. Any other wiring would have resulted in the other kitchen outlets being live only when the switch for the disposal was on.

You cannot split a GFI outlet. I don't know how you attempted to wire this but I suspect that you attempted to reproduce the wiring of the old outlet. I also suspect that you did not realize that the white wire going to the switch was not a neutral, but is a hot wire. You also probably didn't realize that the old outlet was split.

Suggest putting the old outlet for the disposal back. The disposal does not have to be GFI protected. Replace the next outlet in line with the GFI

That still doesn't determine what is wrong. A GFCI only trips on a ground fault, not an overload so it could still be the outlets or the disposal. The wired outlets in the kitchen should have been protected by a GFCI. Are they? If the lead to the disposal goes from that GF outlet to another GF, it will trip it. Can't have 2 GF's on the same line. You can wire GFCI's 2 ways, line-line or line-load. Many people wire the GF to the outlet and then load side everything else. Not a good idea with lighting since you also lose the lights if the GF trips. Run the power to the line side and then the other outlets or lights from the same line side, unless you are required to GF all the other outlets. If you want to protect ALL outlets on the same line, run power to the line side and then run the rest of the outlets off the load side. As TK says, code does not require a GF on a disposal.

You cannot split a GFI outlet like you can a regular outlet.

If you take power to the switch and then to the GFI outlet you only have power to the GFI and subsequent outlets when the switch is in the on position.

If you take power to the GFI outlet and a switch leg to the switch, you can either pigtail off the hot wire or wire from the line side of the GFI to the subsequent outlets but they will not be GFI protected. If you wire from the load side of the GFI the subsequent outlets will be GFI protected but they will be live only when the switch is in the on position (just like the GFI outlet).

Therefore a GFI will not work in this location.

Tell us how you attempted to wire the switch to the GFI.