The simplest deletion command is x. It deletes the character under the caret. A count before deletes that many characters, e.g. 10x deletes 10 characters. Similarly, the X command deletes one character to the left of the caret.
The D command deletes from the current location to the end of the line.
The d command is an operator and thus must be combined with a motion command. For example, dw deletes a word, d3W deletes 3 big words, and dd deletes the current line.
The c (change) command is similar to the d command, but also enters insert mode.