I'm the same. If you can, take off the rear view mirror, usually just slides in to place. If you've got auto lights, don't bother. Just gives you a little bit more access.
I personally use Koch Chemie glass cleaner, but any glass cleaner will do the trick. Auto Glym Fast Glass is good stuff and readily available.
Then use a clean glass specific microfibre cloth, if you've not got one a short pile microfibre will do the trick. Give it a good buff all over, then finish in straight lines. Once you've done this and removed any smudges / dirt, I use another clean cloth, or a lint free paper towel to buff off.
That should do the trick
As above, any decent exterior glass cleaner will be fine. Clean, dry cloths at every turn and most importantly whenever possible leave the doors open for a short while so that any alcohol residue can evaporate. Make sure you do it after cleaning the dash and carpets as disturbing dust and fibres will only dirty the glass again