You already know about the DEL key which deletes the character before point (that is, before the cursor). Another key, Control-d (C-d for short), deletes the character after point (that is, the character that the cursor is on). This shifts the rest of the text on the line to the left. If you type C-d at the end of a line, it joins together that line and the next line.
To erase a larger amount of text, use the C-k key, which kills a line at a time. If you type C-k at the beginning or middle of a line, it kills all the text up to the end of the line. If you type C-k at the end of a line, it joins that line and the next line.
See section Deletion and Killing, for more flexible ways of killing text.