You need a graphics card, if he's not doing any 3d calculations (modelling, gaming etc.) then any with the appropriate outputs for your monitors will do so you're looking at £25-35.
To fit a low power graphics card like that you need to check whether your system has a PCI-E 16x slot (to fit it in) and whether the system is normal width or low profile (if it's the latter you have to make sure the card comes with a low profile bracket).
The link to the specs you've posted seems to be garbled data as a lot of them are nonsense but there are much more helpful documents on the
dell website, they confirm the Vostro 230 has a PCI-E 16x slot but they also say it comes in two different cases. In
this document the "Mini Tower" is the normal case and any graphics card will fit and the "Slim Tower" is a low profile case and you need a low profile card that includes a low profile bracket in the box.
As to connections, DVI and HDMI will plug into each other either way round (so DVI on the card to HDMI on the screen or HDMI on the card to DVI on the screen) as well as straight connections and a DVI output on a card will generally also output VGA. VGA ports on the card can only be connected to VGA ports on the monitor.
Something like
this is what you're after, with it specifically stating the low profile bracket is included and ideally two digital outputs as they'll be best if the monitors have them (HDMI and DVI are digital, VGA is Analogue). If
You can get USB "Graphics cards", but they're generally slightly more expensive and as the Vostro doesn't have USB3 then they're not going to be as smooth as a normal graphics card, especially if the monitors are medium resolution ones (1920x1080 for example).