If this is single player. there is a program called ATMA (see
here) which allows transferring stuff between characters and even storing all your finds away from your stash or inventory - and the best item drop calculator I know.
If you are playing on battlenet, you have to create a game (with a password !!) and wait 5 minutes. After that time it will persist for up to 5 minutes without anybody being in, so you can drop stuff and enter it with another character. There are a few things to consider:
1. Sometimes games crash. If that happens after you left the game with the character who dropped the stuff, your items will be gone.
2. Before dropping stuff, leave the game, wait 3 seconds and enter again. Sometimes you will have a typo in the usual name of the game respectively its password. In that case, the game will be deleted after 5 minutes with your items being gone if that happens with expensive stuff lying on the ground.
The best way is to have a 100% trustful friend or you have two instances of the game. You need two sets of keys and either WinXP with 2 (Windows) user accounts plus Diablo installed separately for each one or two computers for that. In that case you can pass stuff via the trade window which is considered safe, even when a game crashes.