Under the ice:
Under the ice on Europa, there is... more ice. The upper layer of the planet is actually a solid ice layer, similar to the upper mantle of the Earth. While solid, there is a lot of convection (on Earth this creates tectonic activity), so if you drilled a tunnel down there, it would collapse pretty quickly due to the shifting ice. Also, as you drilled down there would be lots of pressure from the gas formed by sublimating ice that you've newly exposed to the vacuum of space.
So vehicles designed to go down there would have their own drilling equipment and be able to fix themselves to the ice, maybe using giant spikes or equivalent. If and when they get down to the water level, they would probably stay as close as possible to the surface to avoid getting caught in underwater currents caused by the tides (when you orbit a gas giant, your tidal forces are very, very strong), so I doubt you'd even have a submarine-like design, just a tank that claws its way through the slushy ice-soup that saturates the top levels of the oceans.
On the surface:
Easy peasy. Europa's gravity is about 13% of Earth's, so you could propel yourself with jets of water vapor expelled from RCS thrusters:
Water vapor is easy to make when the ground is made of ice and you have nuclear power. 208
Don't bother with hydrogen and oxygen: just superheat the water and explosively blast it out of a nozzle: the easiest way to store hydrogen and oxygen is in the form of water.
Local materials:
Well, you're good on fuel. Everything else would have to be imported or slowly fished out from the ice's mineral content through electrolysis, dew point separation, or whatever ends up being more efficient. There's a good amount of carbon down there, and plenty of hydrogen, so you could conceivably make plastics through a convoluted and power-hungry process. Some metals are present at impact sites, as well as silicon, which you could use to make ceramics. You might be better off importing though. It depends: if Europa is a fuel-mining colony, they can probably afford to filter their water for impurities as part of the refining process. If they're a research outpost, haha good luck! 778