How to check which database objects are using certain tablespace in Oracle DB

The answer to your question can be found in the SQL Language Reference (excerpt follows).

Creating Basic Tablespaces: Examples

This statement creates a tablespace named tbs_01 with one data file:

CREATE TABLESPACE tbs_01 DATAFILE 'tbs_f2.dbf' SIZE 40M ONLINE;

It sound like you are new to Oracle databases. Oracle provides a wealth of documentation at http://docs.oracle.com/en/database. Specifically, I recommend reading their excellent introduction to the database called the Concepts Guide.

17:31:15 SYSTEM@sandbox> ed
Wrote file S:\spool\sandbox\BUFFER_SYSTEM_34.sql

  1  select sid,  process, program
  2    from v$session s join v$bgprocess using (paddr)
  3   where s.status = 'ACTIVE'
  4*    and rownum < 5
17:31:21   5  /

       SID PROCESS                  PROGRAM
---------- ------------------------ ----------------------------------------------------------------
         2 1332                     ORACLE.EXE (PMON)
         3 480                      ORACLE.EXE (PSP0)
         4 976                      ORACLE.EXE (VKTM)
         5 992                      ORACLE.EXE (GEN0)

Elapsed: 00:00:00.05

However, this doesn't make much sense as they're always stated as active, so I guess you should define what you mean saying active.