How to create joint accounts in CiviCRM contacts
The short answer:


When you want to store information about two people (e.g. "John Smith" and "Mary Smith") together, create a new household.
You can name the household whatever you like (e.g. "John and Mary Smith", or "Mary Smith and John Smith", etc)
Add shared information like home phone number (land line) and home address to the household record.
Also create individual records for each of these people. Now you have three contact records.
Create relationships between the individuals and the household. You can also set up the individuals to use the address of their related household.
Add other data to the individuals which is specific to them personally (e.g. cell phone, email, birth date, gender, etc.)


The long answer:

While you're in this phase of deciding how to store your data in CiviCRM, I would suggest first taking a step back and considering why you might need to store data associated with multiple people, and if it's worth it to use households at all (because some organizations choose to disable them entirely and only use individual/organization records). For example:


Contributions:


When using households: If you receive a check with two names on it, an intuitive approach is to store this contribution on the household record.     
When using only individuals: Another approach is to store it on one individual and soft credit the other one.

Event participations:


Regardless of your household strategy, it's best to keep event participations on individual records.

Memberships:


You can store memberships on household records or individual records, or some combination thereof. How you choose to do so will likely depend on your overall membership strategy

Relationships


When using households: relationships are created between individuals and their shared household. This makes it somewhat cumbersome to navigate from individual to individual because you must first navigate through the household
When using only individuals: you can set up a relationship type like "Spouse" to store the connection between two people and easily navigate between their records

Combined solicitations:


When using households: If you are sending a paper mailing, you can use CiviCRM to generate a mailing list which uses households to group contacts together and avoid duplicate mailings.
When using only individuals: grouping related individuals into the same mailing piece will be more difficult and probably require some custom work
This, in my opinion, is the biggest argument for using households

Keeping your data clean:


When using households: 


Creating the requisite relationships and extra records is more work
De-duping is somewhat more complicated
When two people split up, it can be a pain to figure out what to do with their household record

When using individuals:


De-duping is simpler 
Setting up the relationships requires fewer steps
Relationships can be disabled (even with an end date)