Although your water pressure may be low, you can still wash your dishes efficiently, either by hand or by using a washing machine. The level of water pressure should not affect how well your dishes are washed.
If you don't like the low water pressure in your kitchen, change it. Check the pressure on the hose bib in the front of the house. The problem may be as simple a fix as setting it higher. Inspect the tap in the sink; the screens may be clogged with hard mineral deposits. Clean them out completely. If you have a pressure reducing valve for your water, get it adjusted by a professional plumber. These are devices located near your hot water heater.
Always rinse the dishes before putting them in the dishwasher, which takes care of large food chunks. If you don't want to run the water to rinse the dishes, simply scrape them with the silverware into the sink or garbage. Placing your silverware into the basket with the tines and sharp points facing down will prevent your fingers from getting poked when you unload the dishwasher. Place the cups and small items in the top of the dishwasher and the plates and bowls in the bottom, facing towards the water jets. Load the soap dispenser and start the dishwasher.
Fill the sink halfway with hot soapy water. If any of your dishes have caked-on food, put them in the sink first, which will allow them to soak while you wash the remainder of the dishes. Any loose food particles should be scraped into the garbage can before placing them in the sink. Use a washcloth or scrub brush to wash up the silverware, plates, bowls and cups. You'll want to rinse the dishes in hot water, running the water over the soapy water sink so you are continuously adding hot water to your washing water. Allow the dishes to air dry on a drain rack or kitchen towel.