My printer doesn't up. I just hooked up my printer to my computer. I'm done installing and clicking "next" "next" thing even if I didn't see the exact words "HP Deskjet 3745" on the selection. I just entered the word manually on the following page.

Printer is on and when I'm it seems like the ink is responding if I'll hit on and off the green light on the printer but doesn't do anything more. Please help.

You can't just write in the printer name. You NEED to select the correct printer from the list OR use the correct drivers. What version of Windows do you have?

I don't know why the exact name of the printer isn't on the list. When I chose HP, it populated me the list of HP units and HP Deskjet 3745 isn't on the list. My windows is XP.

Ok, the DJ 3745 is not included in the supported printers for XP. So you need to install from the CD that came with the printer. If you don't have the CD, then you can download the drivers from here:
Select software and drivers

After downloading the file, just run it. For further instructions.