We know you'll be desperate to make a statement in your stylish suede watch, but first we highly recommend using a suede protector to reduce risk of staining.
If your suede strap gets dirty, it can be brushed very gently with a textured cloth or super-soft toothbrush, in the direction of the nap (that's the suede fibres). You may want to consider a specialist suede brush and eraser.
Brush regularly to keep your suede straps soft & supple.
What if it gets wet? Just let it dry naturally, then gently brush out the nap to restore to former glory.