My partial mash method:
1) Put crushed grain in a sack through the mash temp schedule
until the desired preboil/pre-DME OG reading is met.
2) Place grain bag in a large colander over the kettle and raise wort temp. Two washes with 165 deg wort (usually adds 1% Brix or so) and a final wash of 165 deg water.
3) Raise temp of diluted wort to at least 180 deg. Add DME, if any.
4) Fill partial kettle the rest of the way and boil.

Lagering schedule:
1) Cool wort as normal but do not immediately pitch yeast. Cool in lagering fridge 4-6 hours towards target 50 deg F.
2) Rack a gallon or so of wort, pitch yeast and splash back in to aerate a bit more.
3) Ferment for 2 weeks at 50 deg F.
4) Unplug the fridge for 3 days for a diacetyl rest.
5) Transfer to secondary fermenter and start dropping the fridge temp from ~65 to 34-48 def range in steps of 4-5 deg per day. Lager as long as you want, minimum additional 2 weeks.