If you do not have access to the email associated with your Steam account, you'll need to contact Steam Support to reset your password.
If you do not know your current password, you can still reset your password yourself at https://help.steampowered.com
Open the Steam client and go to Settings (Preferences on a Mac):
Select "Change Password...":
Enter your current password:
(Don't remember your password? You can use the Help site to reset it)
An email from Steam Support will be sent to the email address associated with your Steam account. If you don't receive an email, make sure to check your spam folder.
Enter the 5 character code from the email and enter a new password. NOTE: It must not be a previous password and must meet the password strength requirements.
When you've completed changing your password, you'll receive confirmation by email.