You can use .length, like this:
var count = $("ul li").length;
.length tells how many matches the selector found, so this counts how many <li> under <ul> elements you have…if there are sub-children, use "ul > li" instead to get only direct children. If you have other <ul> elements in your page, just change the selector to match only his one, for example if it has an ID you’d use "#myListID > li".
In other situations where you don’t know the child type, you can use the * (wildcard) selector, or .children(), like this:
var count = $(".parentSelector > *").length;
or:
var count = $(".parentSelector").children().length;