Mutt's configuration is sometime more a toolbox than something offering ready solutions, and "how to I use multiple accounts?" is one of the most FAQs. Here's a condensed version of my setup.

In the most simple solution, just 'c'hange folders to the IMAP server:

c imaps:// <enter>
c imaps://imap.otherdomain.tld <enter>

That's cumbersome to type, so let's automate it:

# .mutt/muttrc
macro index <f2> '<change-folder>imaps://<enter>'
macro index <f3> '<change-folder>imaps://imap.otherdomain.tld<enter>'

That would be the basic setup.

The two accounts have settings associated with them, we put them in two files:

# .mutt/account.example
set hostname=""
set folder="imaps://"
set postponed="=Drafts"
set spoolfile="imaps://"
set signature="~/.mutt/signature.example"
set smtp_url="smtp://" smtp_pass="$my_pw_example"

# .mutt/account.otherdomain
set from=myself@otherdomain.tld
set hostname="otherdomain.tld"
set folder="imaps://imap.otherdomain.tld/"
set postponed="=Drafts"
set spoolfile="imaps://imap.otherdomain.tld/INBOX"
set signature="~/.mutt/signature.otherdomain"
set smtp_url="smtp://myself@mail.otherdomain.tld" smtp_pass="$my_pw_otherdomain"

Now all that's left to do is two folder-hooks to load the files:

# .mutt/muttrc
folder-hook '' 'source ~/.mutt/account.example'
folder-hook 'otherdomain.tld' 'source ~/.mutt/account.otherdomain'
# switch to default account on startup
source ~/.mutt/account.example

A slight variation of the macros also uses the account files:

macro index <f2> '<sync-mailbox><enter-command>source ~/.mutt/account.example<enter><change-folder>!<enter>'
macro index <f3> '<sync-mailbox><enter-command>source ~/.mutt/account.otherdomain<enter><change-folder>!<enter>'

To save entering the password all the time, we use account-hooks:

account-hook 'set imap_user=me imap_pass=pw1'
account-hook otherdomain.tld 'set imap_user=myself imap_pass=pw2'

Putting passwords in configs isn't something I like, so I pull them from the Gnome keyring:

set my_pw_example=`gnome-keyring-query get mutt_example`
set my_pw_otherdomain=`gnome-keyring-query get mutt_otherdomain`
account-hook 'set imap_user=me imap_pass=$my_pw_example'
account-hook otherdomain.tld 'set imap_user=myself imap_pass=$my_pw_otherdomain'

(I found gnome-keyring-query in the Gentoo Wiki.)

Martti Rahkila has more verbose article with similar ideas.

Update 2013-01-02: smtp_url and smtp_pass added