Anyone good at washing dishes? I need advise.

I grew up with a dishwasher and while I've lived without one before, this is the first time I've been without one while having a 9-5 job. I tend to get way behind. Obviously a good part of that is avoiding a pile-up in the first place.

However, I think the other part of the equation is that my technique is half-assed. Fairly often I'll need to rewash dishes I've put on the dryer rack lest they feel wrong.

My basic technique at this point:

1. Put some dish soap on the sponge.
   
   
   
   1. Rinse the dish.
   
   
   2. Scrub off any crud with the green part of the sponge.
   
   
   3. Give the entire dish a once over with the green part of the sponge or dish rag.
   
   
   4. Rinse the dish again. If suds remain, repeat rinse until they're gone.
      
   5. Place dish on drying rack.
      
   
   
2. Loop until bored, drying rack is full, or out of dirty dishes.
   

Late on I'll deal with the dry dishes.

1. Put away dry dishes.
   
   
   
   1. If dry dish feels sticky or has soap scum, rinse it again.
      
   2. If actively unclean, place it back in the sink.
      
   3. Dry dish with towel.
      
   
   
2. Loop until out of dry dishes or bored.
   

Could be I just need to be a lot more diligent about my cleaning. But I also wonder if my technique is wrong. Should I invest in a brush? Should I be changing sponges more regularly? As is, the task never really feels done, so it's hard to get myself motivated.