How organized was the journey home? Would our lord guide us home? What if the group I initially served under had been absorbed into another group? How well equipped would the average soldier be to return home after serving in a foreign war?
As with so many questions regarding the Middle Ages, the answer depends on where and when. Remember, "medieval" covers nearly a thousand years of time and--even if we restrict ourselves to Western Europe--many different cultures.
Even the nature of a "peasant recruited for a war" changes. For example, in Angle-Saxon England (say 10th to mid-11th century), a freeman (note freeman--serfs and slaves were exempted from this) was required to turn up under arms when summoned to serve for a set period of time in the Fyrd (sort of like a militia). You provided your own weapons and armor, and how you got to the rendezvous point and back home after being dismissed was your own responsibility. But, with rare exception, the distance from home wouldn't be that great. Mostly, you'd be summoned to the Fyrd to defend your shire, and even if you are launching an invasion, it would be more of a journey of a distance from London to Cardiff, not London to Constantinople.
Now, compare that to England in the mid-14th through the early 15th centuries. Here, the peasant soldiers are, again, predominantly freemen who provide their own arms and armor, but now they are paid volunteers who join up in exchange for a set wage paid by whoever is leading the expedition (for example, King Edward III leading a expedition into France in 1346, or Henry V in 1415). And their enemies at this time, the French, used a somewhat different system for raising their armies, which was different from the system used in the Italian city-states, which was different from the system used in the Byzantine empire...etc.
Travel in the Middle Ages was was both more difficult than today and, in a way, more straightforward. Instead on navigating by points of a compass, its more by what towns and landmarks you should pass by to get from point A to point B, and what routes you take (e.g. roads, rivers, valleys). There weren't really much in the way of useful maps for this, so if you were trying to get somewhere from somewhere else and were not familiar with the route, you'd be doing a lot of asking for directions in addition to following whatever major travel route (like a main road or large river) you can.