Wait for the area to dry out. Patching up concrete that is wet doesn't work well and the patch is likely not to hold. There is a cause for the wet floor, whether it is a plumbing leak or heavy rains. Have someone repair any leaks, or wait for the rain to stop. The ground water is going to have to subside somewhat or you to patch it. Once the rain stops or the leak is fixed, help the drying along by setting up fans to circulate the air. If there are window, open them for a cross breeze.
Scrub the floor with a brush and rinse with water while it is still wet. The extra water won't hurt and loose debris has to be removed before a repair can be started.
Mix cement and water in a bucket to the consistency of paint. Mix concrete patch in a separate bucket, following the directions on the package to ensure success.
Paint the cement mix into the crack with a paintbrush. The cement will help bond the old flooring to the new patch material.
Pour in the patch mix while the cement paint is still wet. Level is smooth with a scrape and wipe up the excess. Let it dry overnight.
Wet the patch the next day to slightly dampen it. This will help cure the patch and make it harder. Wet it once a day for three days.