If you have a lot of dishes that you have washed by hand, you can stack them on a multi-shelved rack as shown in the picture, and let them drip-dry. Shelves like this can be found at a hardware store (they are not usually used for drying dishes).
Place a towel in the bottom shelf to catch the drips.
Place cutlery in a colander or on a tea-towel so it doesn't fall through the gaps.
Fill the lower shelves first; sit a lower shelf on the top shelf while you are filling it with dishes.
Finally, fill the top shelf with the most bulky items.