Take the remote apart and remove the rubber membrane that has the buttons moulded. Wash it with warm water and normal washing liquid. Be gentle, don't scrub too hard, if required soak for a little while. Shake well and blow off any excess water. Air dry it well, but don't use towels or other cloth/paper that may leave hair, fibres or dust on the rubber.
Get some WD40 and cotton buds. Put a few drops of WD40 on the remote control PCB and use the cotton buds to carefully clean everything. The WD40 will displace any residual moisture and other gunk and the cotton tips will absorb everything. At the end of the cleaning process, the PCB should be shiny clean and not soaked in WD40. Use the cotton tips to wipe of any excess WD40. You should clean both sides of the whole PCB, including the pins of the ICs and the gaps in between.
Next, use a very soft pencil on the PCB pads where the rubber membrane buttons make contact. You want to be very gentle and put a very, very fine coating of graphite on these pads. This improves the contact, since graphite is conductive. Be sure that you don't scratch off the PCB pads with the pencil. Also make sure that the coating is very thin and that you don't clog up the pads and cause a permanent short.
Let everything dry out for at least an hour, reassemble and enjoy a remote that's hopefully as good as new.