How can I connect two USB printers HP laserjet P2035n and Brother HL-5340 D-series) to a single computer HP Pavilion gv9999) running on Vista?

Shouldn't be a problem.

Use an active usb hub(one that has a power supply) plug one printer in each hub slot and then 'look' for them with printer set up should see them both

Be aware that many printer instructions tell you to install their software before you plug in the printer so that Microsoft doesn't install it's own first. Then once the second printer is installed and plugged in, go into the control panel and open the printer icon and select add printer. One of them will have to be default though, it won't print on both at the same time. A lot of the time when I install printers I do not use the software they provide, and choose (if they let me) drivers only. It would be a good idea to do that with the second one. Also it would be advisable to set a restore point before you start so you can get back if there is a conflict. System Restore works best from safemode.