Before you remove a sink trap, give the drain a few plunges with a toilet plunger. This will push most of the water out of the trap and will lessen the mess when you pull the trap.
If you have a double sink, be sure to plug the other drain to contain the air pressure. You may have to hold it down while you plunge the drain if the strainer isn’t a screw-down style.
Keep in mind that you should never pour hot grease down the drain as over time, the grease may get hardened and require a technician to repair the issue.