Most highchairs are designed to be easy to clean. Scrub with a hard brush and some magical pixie dust AKA baking soda. Make a solution of baking soda and castile soap (50/50) with a bit of water.
Once its scrubbed clean hose it down to get in all the sides etc. Do this on a sunny and hot day so all the parts dry very quickly.
Same principle works on prams - I make a thick paste and rub it in with my fingers, leave it for five minutes and then scrub with a hard bristle brush. Then you simply hose down and sun dry.
You can also use this magical pixie dust to get stubborn stains out of car seat fabric, and then just put the whole thing in the washing machine.
I use this very same solution to clean my bathroom, the kitchen sink, take dirty fingerprints off paint - you name it. The great thing about it is that I never worry about the kids getting into my stash of cleaning products. Baking soda is a cooking ingredient, and the Castille Soap is what we have in our bathroom*!
*In earlier centuries, an all-vegetable based soap was made in the Castile region of Spain from local olive oil. By the turn of this last century, "Castile" had come to mean any vegetable oil-based soap, versus animal (tallow) fat-based soap. Castile Soaps are a pure and simple liquid soap, not a complex blend of detergents. Castile Soaps do not contain any synthetic foaming agents or detergents. We use Dr Bronner Castile soap. You will find it at your local health food shop.