I want to take vector because it rezises perfectly for any screen resolutions your players might have.
I will make it to the gui at character creation.
I will use program called inkscape (inkscape.org).

I just don't know like.. what type of file should I save the vector art as? is it possible to make it to PNG or DDS?
Won't it become a normal image if you export it like that? And losing the benefit of it being vector.

And how do I add it to the game? What file must it be etc?

Do you know any good tutorials that is related to what I want to do that I can have any use of?

is it possible to make it to PNG or DDS? Won't it become a normal image if you export it like that? And losing the benefit of it being vector.

And how do I add it to the game? What file must it be etc?

Yes, PNG/DDS are bitmap formats, not vector formats.
Valve do actually export their vector art in bitmap format, by encoding it as a signed distance field, and reconstructing the edge in a pixel shader.
http://www.valvesoftware.com/publications/2007/SIGGRAPH2007_AlphaTestedMagnification.pdf


The last game that I worked on with vector art used SWF (flash) files, but you could also use SVG files.
To use them in your game, you'd download/buy/build a SWF/SVG file loader and renderer. There are open source and commercial solutions.

Inkscape can save directly to .SVG format. (And if you have a good understanding of the svg format you can open the svg files in a text editor and manually tweak them as well).

Getting them into you game will require a loader / renderer API as Hodgeman said. Which one will depend on which language you are using for the game. For instance, if you were using Java I would suggest taking a look at Batik: http://xmlgraphics.apache.org/batik/

Thanks, The engine I use is hero engine if you got advice specific to that one.

Is there a way I can look if this engine support SVG format.. Do I need to find a renderer api if I use hero engine?

edit:
it says in wiki that the only texture formats for hero engine is DDS and PNG.
So how do i do then?

You don't. Picking an engine includes picking its restrictions as well as its features. Unless you are able to modify the source code of the engine and/or its various asset creation tools, this is something you can't do with your selected engine.

Since you're using Hero, why bother with the vector art, honestly? In most game UIs, if the player increases resolution, the resulting bitmap UI elements just appear smaller (and often cleaner, but I guess that's more of a personal preference).