Having a PCB manufactured requires two steps: 1) Create the files, and 2) Send the files to the PCB manufacturer.
Route the board (using autorouter)
Check for design rule violations (Design→DRC and Netlist Check).
Check that all connections are complete (Design→Connectivity Check - then check "All Nets"
Export the necessary Gerber file (objects with shapes):
Select "Gerber RS-274X" and hit the "Properties" button
Check the "Board Outline" box under options, and
move "Copper Top" and
"Copper Bottom" to "Export Layers." Hit the "OK" button.
When you get back to the "Export" dialog box, hit
"Export" and save the two files (one for the top and one for the
Export the necessary drill files:
Select "NC Drill" and then hit "Export" and save the two files (the .ncd file specifies the location of the holes (this is an "Excellon drill file"), the .rpt file specifies the sizes of the tools used to drill the files (this is the "Tool list").
These are all the files needed to manufacture the board.
Do as described above, but in step 4 also add the layers "Silkscreen Top," "Solder Mask Top" and "Solder Mask Bottom."
I usually use APCircuits.com which gets the boards back in about 3 days and you can use a college purchase order. The cost is about $50 to $60 for two 3"x4" boards (you need to order an even number). You can zip the files together and send to APCircuits (see their web page for details). I use their free program "APClient.exe" (available on their web page) which prompts you for all the information they need.
You can use APCircuits.com (typically $80 to $100 for two 3"x4" board) using the procedure above. It usually takes about a week.
If you are a student, you can use 4PCB.com (see their web page for details about how to submit the files.). They usually have a promotion going that will give you a single board for $33 (again, in about a week), and they often send a small gift (popcorn, pizza coupon, T-shirt...). They won't take a college purchase order.