Dishwasher does not clean well. What DIY advice do you have?

Usually this means that the dishwasher is not draining well.  The drain hose may be kinked, or the screens or pump or macerator could be clogged.  The pump may be bad and need to be replaced. 

As a renter, this is really your landlord's problem, as they are responsible for all repairs unless your agreement says otherwise.

Water may not be hot enough. If d/w is far from hot water tank, water may not be heated warm enough by the time d/w fill valve shuts off. Many good dishwashers have a heated water option. If yours does , try it. Finally: Cheap d/w without multi level cleaning don't work well. Also, there is often a rinse only cycle which gets rid of heavy food deposits, so they aren't dried hard on the dishes when you are ready to do a load.

The drain is the problem, find where the hose enters the drain, whether it enters it's own drain pipe or the side of the disposal or an airgap that is connected to the top of he sink.  Disconnect the hose clean both internal areas, hose end and where ever the connection is inside that drain as well, even if you use a flat head screw driver clean it really well.  reconnect it and run it thru a drain cycle a couple of times this should rinse out the remainder of what ever was plugging the drain.  If the air gap is completely clogged the water when the D/W drains, water will come out, if it is a air gap that protrudes thru the wet side of the sink, be sure the air gap is cleaned on both sides.   I totally agree with Bob with it being a rental, call the landlord, let him do it.