In an extremely rough and simplified sketch, assuming the simplest possible
HTTP request, no proxies and IPv4 (this would work similarly for IPv6-only
client, but I have yet to see such workstation):

1. browser checks cache; if requested object is in cache and is fresh, skip to
   #9

2. browser asks OS for server's IP address

3. OS makes a DNS lookup and replies the IP address to the browser

4. browser opens a TCP connection to server (this step is much more

   complex with HTTPS)

5. browser sends the HTTP request through TCP connection

6. browser receives HTTP response and may close the TCP connection, or

   reuse it for another request

7. browser checks if the response is a redirect (3xx result status codes),

   authorization request (401), error (4xx and 5xx), etc.; these are handled

   differently from normal responses (2xx)

8. if cacheable, response is stored in cache

9. browser decodes response (e.g. if it's gzipped)

10. browser determines what to do with response (e.g. is it a HTML page, is it

    an image, is it a sound clip?)

11. browser renders response, or offers a download dialog for unrecognized

    types

Again, discussion of each of these points have filled countless pages; take this
as a starting point. Also, there are many other things happening in parallel to

this (processing typed-in address, adding page to browser history, displaying
progress to user, notifying plugins and extensions, rendering the page while
it's downloading, pipelining, connection tracking for keep-alive, etc.).