Whenever I try to delete a file in Finder I get "Finder wants to make changes. Type your password to allow this."
OS X asks for a password whenever you try to delete a file because your ~/.Trash folder belongs to the root user and has permissions drwx------ — noone but root can read, write or open this folder. Being in the same situation I tried the command shown below in Terminal and it helped:

sudo chown -R steve:staff ~/.Trash


Note that I've changed my username to yours in this example. Also note that sudo command will ask you for user password — it's OK.