There are a number of different index types in different database systems, for the purposes of this reply though I'm mostly going to refer you the wikipedia discussion on B-Tree indexes because that is almost certainly the index type you mean. (nb to commenters I know that the trees aren't strictly b-trees but that doesn't matter for this discussion) This type of index will be created by sql statements such as
create index idx_t1_c1 on t1(c1);
In a B-Tree index the data is stored in a ordered tree, where the highest (or root) pages just have pointers to lower level branches which in turn have pointers either to lower branches or the lowest level pages(or blocks) that themselves hold pointers to the table pages that have rows that contain the indexed value. Retrieving indexed data via an index then becomes a matter of walking the tree down from the root via pointers all the way to the leaf(s) containing the value you are interested in. If you then need to go to the table you have direct access to the pages you need rather than having to scan the whole table. This mechanism is entirely independent of the datatype of the indexed column. The internals of Oracle vs SQL Server are different and protected by IPR, but the logic is essentially the same. The efficiencies come because typically the depth of the index will be quite low (2 or 3 levels for the vast majority of typical segment sizes) and the number of leaves containing values of interest will also be low so you are likely to be able to filter for the data you are interested in in only a handful of i/o operations rather than scanning the entire object.
If you really are interested in on disk storage then the commands below can be used to dump representations of the pages to disk for inspection. If you do this and are not deeply familiar with data structures from some formal information technology education you may regret it :)
ALTER SYSTEM DUMP DATAFILE <n> BLOCK MIN <x> MAX <y> ; -- oracle file n, block x->y
DBCC PAGE (DBID,FILENUM,PAGENUM,<LEVEL>); -- mssql -- level 0 to 3 increasing detail