Wipe clean with a damp cloth and dry naturally. A neutral protective leather cream can be applied, and this will not affect the waterproof qualities of the shoe. Gently buff with a clean cloth or brush. Both a neutral cream and a neutral polish are useable. However, as this is a casual style, a cream is preferable as it will maintain the characteristic of the leather. A polish will, over time, make the leather a little glossier / dressy in appearance which will change the look of the shoe.
A colour polish could be applied, but please note the shoe features contrasting stitching and this would gradually change the colour of the stitching and you will probably find it difficult to buy a polish to match the colour of the shoe/boots.
If preferred, use a waterproof or water-resistant cleaning/protective spray to help maintain the natural look of the leather.