How do I assemble a using jQuery append()?

Nope, you can’t use it like that. append is an atomic operation, which creates the element directly.

// The <ul> element is added to #details, then it is selected and the jQuery
// selection is put in the "list" variable.
var list = $('<ul/>').appendTo('#details');
for (var i = 0; i < 10; i++) {
    // New <li> elements are created here and added to the <ul> element.
    list.append('<li>something</li>');
}

Alternatively, generate the HTML and add it all at once (this will be more similar to your original code):

var html="<ul>";
for (var i = 0; i < 10; i++) {
    html += '<li>something</li>';
}
html += '</ul>';
$('#details').append(html);

This code is noticeably faster when dealing with many elements.

If you need a reference to the list, just do the following instead of $('#details').append(html);:

var list = $(html).appendTo('#details');