Begin by gently brushing off any excess grime with a soft brush or cloth (with a little warm soapy water if it helps – do not soak the brush or cloth) and recondition them with a good leather care – like Nik Wax leather conditioner, alternatively, use a quality dubbing or leather creme / conditioner – applied evenly with a soft brush.
Always let the boots dry naturally, away from direct heat sources. If you want, remove the laces and clean any excess dirt and grime from all parts of the boot. When dry, the laces can be sprayed with silicone to stop them rotting.
The waterproof and breathable membrane is a ‘bag’ behind the lining within the boot, so be careful to not use any sharp objects that may push through the inner lining or outer construction and pierce the membrane.