ok, let's start off:
Use toolkits
First you would want to invest time learning a JS toolkit. While others suggest native JS is good (which it really is), but you would not want to waste time on building apps that don't work cross-browser or spend too much time testing it. People in the community have invested their time in doing that for you. Show some love to the open community and use their product. I personally use jQuery, but there are others like Dojo and YUI.
But still use native JS whenever possible. It's still faster.
Structure your code
After a toolkit, you need some structure. BackboneJS will take care of that. It's to structure your code so that your code is reusable and well.. won't end up as spaghetti on your screen. Other tools like RequireJS are also useful for those scripts that need other scripts to run.
Templates: From strings to elements
Then, with that, you now have a toolkit but you still need to build the interface. It's better if you use a templating engine like Mustache or Handlebars. These render templates for your UI from strings (yes, plain strings of HTML). Just send over your template data from the server, store it in your app (in a variable or browser localstorage), and reuse it as necessary. No need for cloning hidden nodes!
Don't touch that DOM
As for approaching the DOM, you should touch the DOM only when necessary. DOM is slow, manipulating it is he** slow! that means you should avoid unnecessary animations, avoid excessive element append and remove, as well as changing styles. Check this article about avoiding too much reflow and repaints. Face it, the user won't event notice the round corners of your boxes, or the gradient background and don't even care if you did a slide animation or a fade-out. What they want is to get the job done and not adore the fireworks display.
Also, remove anything that isn't on screen. You might end up having 20% content on screen, and 80% off screen - a waste of memory.
Cache: fetch once, store, use infinitely for later
Now, your app is getting heavy and you want to shave off some HTTP requests. You can do this by caching. I usually use caching mostly on the templates so that every new UI, you don't need to load again from the server. You can do this by storing stuff in an object. you can go a little further and use the browser's localStorage when available.
Caching isn't all for the network. Let's say you have some complex calculations you want to use later, or some text from an unfinished form, use the cache for that too.
Avoid HTTP requests (or at least lighten them up)
While lightening up your app by using AJAX, you will inevitably be tempted to use AJAX just about anywhere - don't abuse it. Often times i see people who aggressively poll the server (every half-second or less). This not only strains the server (too many requests), but also the browser (wasting processing cycles) and the network (bandwidth). There are several practices done these days to avoid added HTTP requests:
Image Spriting - The art of placing a lot of images into one image and using background-position to change the image. Surely beats 100 individual HTTP requests
Use JSON for textual data - AJAX was meant to use XML.. then came along JSON that was a fat-free, platform-independent format of strucured data.
Do not return HTML-formatted data - With exemption of templates, which are HTML strings, you should never return HTML-formatted data over the wire. Have JS do JSON+templates on the client-side instead.
