You don't need to calculate anything for a Hohmann transfer - just learn to use the maneuver nodes. The only really tricky bit (and the only bit the game doesn't give you enough info to find out on your own without mods) is knowing when you have an easy transfer window that'll only cost a little delta-V.
But he needs to know (at least approximately) the total delta-V he needs for the mission, which means either finding it out by trial and error, or doing a few calculations to find out the required values, which should be the starting point for the craft design. In other words, "How much delta-V do I need for this or that stage of my mission?"
Launch is one thing, and possibly one of the greatest sources of error because sometimes, uh, launches can consume a lot more delta-V than you actually planned. So if you're doing a manned missions, you could try assembling your ship at Low Kerbin Orbit - not only will it be easier to calculate what you actually need from the craft, you can practice rendezvous!
Once you are on LKO just need to have your transit stage, habitat module, possibly separate lander and ascent modules, and return stage. In many cases, transit and return stages are the same on interplanetary voyages, but often you'll find yourself very far from home with a very small spaceship left, just like with the actual Apollo missions. When I (re)constructed my
Saturn-Apollo proxy, I always wonder how the hell the small command module can have enough juice to get home from the Mun, but such are Newton's laws of motion and gravity. Interplanetary travel is slightly more challenging though.
In fact, I've never sent a kerbal further than Minmus, though I've sent unmanned probes quite far.
Nuclear rockets are very, very helpful. Chemical engines should in fact only be used for ascent and descent.
