Use bar soap and a dishcloth. Those fancy detergents really aren't necessary. Simply add soap to the dishcloth the same way that you would to a facewasher to clean your body (with the dishcloth in one hand, and the soap in the other), and wash those dishes!
For scrubbing pots and pans, the same works well, together with a dish scrubbing brush (I picked ours up at the local bargain basement for $2.99). Rub the bristles of the scrubbing brush against the bar of soap, and wash your dishes as normal.
For glassware when you wish to have an extra sparkle, you may choose to add a dessertspoon of white vinegar to the rinse water.
Change to bar soap, and stop those plastic containers going to landfill, or worse still, adding to that Garbage Island in the Pacific. And save money doing it!