How do I change the text of an element using JavaScript?

For modern browsers you should use:

document.getElementById("myspan").textContent="newtext";

While older browsers may not know textContent, it is not recommended to use innerHTML as it introduces an XSS vulnerability when the new text is user input (see other answers below for a more detailed discussion):

//POSSIBLY INSECURE IF NEWTEXT BECOMES A VARIABLE!!
document.getElementById("myspan").innerHTML="newtext";