oil blades regularly and remove hair with a soft brush from clippers to stop over heating. to avoid tram lines, dont put too much weight behind the clippers, or push clippers to hard against the skin. just allow the blades to do the work for you. they should just glide over the skin of the horse. hope this helps.
Also, keeping the clippers on the coat as much as possible reduces tram lines. I.e run them back and forth along the coat rather than clipping a line, removing and clipping another line. Just keep the pressure even and run the clippers backwards and forwards. Hope that makes sense!
Like what saddlesore said, apart from the not digging in, and regular oiling and cleaning, try to do long sweeping movements with the blades and start the next "sweep" slightly overlapping the previous. Then, the all important bit, when you've finished go over the whole coat gently with the blades in a kind of "hoovering" movement, as you would when you vacuum round the furniture!!! I was taught this by a clipping nerd and I have to say it works!