Bus or bike
Oosterbeek is very close near Arnhem, but I recommend the walk only if you're used to distances and hills. The bus will take you there within a few minutes, but it should also be a nice trip on a bike.
Walking and biking
Like I tell on many other pages, in The Netherland you best enjoy the landscape by bike or on foot. The first might be called our national means of transport and many Dutch even have two bikes (one for workingdays and one for the weekend - hahaha). Though in Oosterbeek one has to reckon with the hills (up is hard, down is however easy!), the many bikingpaths make it the best way to get around on short distances (until 25 km).
By train, car or bus
Oosterbeek has it's own tainstation on the line Utrecht - Arnhem. Take a stoptrain as the fast ones do not stop here.
Citybusses from Arnhem bring you quickly to Oosterbeek and also by car it is very easy to be reached.