There are two methods, each with its own advantages and drawbacks.  Try each to learn which is best for you.

Method 1:
Use the "Send a Test Mailing" feature

1.  After defining your mailing's recipients and content, click the Schedule button
2.  In the resulting page, find Send a Test Mailing
3.  Enter each email you want to receive the test.  Separate these with commas or semicolons.
4.  Click Send Test

NOTE: These test mailings can land in your junk mail folder, even if the live mailing would not.  Please check here if you do not receive the mailing within 5 minutes.

Method 2:
Send a duplicate copy of the mailing to only the test recipients

1.  When you have your mailing looking as you would like, check the box next to its name in the list of mailings
2.  Click Duplicate, then OK to confirm you wish to duplicate
3.  Click on the Receiver query link to redefine who should receive the mailing
4.  Click the Remove All button to clear out the list of recipients
5.  Expand Contacts > Profile > Contact Fields
6.  Pick filters that uniquely identify the test mailing recipient.  Email usually works well for this purpose.
7.  Once you have picked out one or a few filters to identify the test recipient, click Preview to confirm that only the intended recipient is picked out
8.  Click Done
9.  Schedule the mailing and choose when you would like the test mailing to go out.

NOTE:  This method actually sends a mailing, but only to the test recipient.  Your recipient must have a contact record in Sphere.  Also, duplicating your mailing ensures you can return to the original once the test is complete.