A partition function gives the ranges to partition by, e.g. if you want to partition by years then your partitions could be
A partition scheme is a mapping of the "parts" of a given partition function to particular filegroups - if you are using the PRIMARY filegroup only, then they will all be mapped there, but some partitions could be on a different filegroup if you want.
A partitioned table has a partition scheme applied to a particular column. For example if your table is "Movies" then you might have a field "ReleaseYear" and all the movies released in 2012 would go into the 2012 partition, etc.
The partition scheme and function can be applied to more than one table, but every partitioned table must have one (by definition), they just don't need to be unique.
However, keep in mind that if you use the same partition scheme/function on more than one table, any changes you make to it will be applied to all the tables, e.g. splitting or merging a partition.
MSDN has some further information on partition schemes here.
Often you will find that you need to index those partitioned tables, and then you'd usually create a partitioned index as well. If it matches the partitioning scheme and field of the "base" table then it is known as apartition-aligned index, which allows special operations like "switching" data from one partition to another without having to physically move all the data.