How to find index is fragmented in Oracle Database?

First analyze index

SQL>analyze index INDEX_NAME validate structure;

Then query INDEX_STATS view
1. If del_lf_rows/lf_rows is > .2 then index should be rebuild.
2. If height is 4 then index should be rebuild.
3. If lf_rows is lower than lf_blks then index should be rebuild.

SQL> column status format a10
SQL> select trunc((del_lf_rows/lf_rows)*100,2)||'%' "status" from index_stats;
status
----------
21.83%

How to remove index fragmentation?

There are two way to remove fragmentation.
1. index coalesce
2. index rebuild

What is difference between coalesce and rebuild please go through below link for more details
http://download.oracle.com/docs/cd/B14117_01/server.101/b10739/indexes.htm#g1007548

SQL> alter index IDX_OBJ_ID coalesce;

SQL> alter index IDX_OBJ_ID rebuild;

SQL> alter index IDX_OBJ_ID rebuild online;

Note: If any DML statement is running on base table then we have to use ONLINE keyword with index rebuilding.

SQL> analyze index idx_obj_id validate structure;
Index analyzed.

SQL> select trunc((del_lf_rows/lf_rows)*100,2)||'%' "status" from index_stats;
status
-------
40.85%

SQL> alter index IDX_OBJ_ID rebuild online;
Index altered.

SQL> analyze index idx_obj_id validate structure;
Index analyzed.

SQL> select trunc((del_lf_rows/lf_rows)*100,2)||'%' "status" from index_stats;
status
--------
0%