how we can save database created in sqlite3

I am trying to create a database and table in it. but unable to save and open again after exiting from sqlite.

You don't need to save. Each transaction writes to disk. (More or less.)

To create the database "test.sl3", you can do this. (From the command line. Programs work about the same way.)

$ sqlite3 test.sl3
SQLite version 3.8.7.2 2014-11-18 20:57:56
Enter ".help" for usage hints.
sqlite> create table test (test_id integer primary key);
sqlite> insert into test values (1);
sqlite> select * from test;
1
.quit

No .save. Now load the database again.

$ sqlite3 test.sl3
SQLite version 3.8.7.2 2014-11-18 20:57:56
Enter ".help" for usage hints.
sqlite> select * from test;
1

The data is still there.

You're supposed to provide a filename as an argument for the .save command, e.g.:

sqlite> .save ex1.db

docs: http://www.sqlite.org/cli.html

as Mike pointed out in his answer, you should provide a file name to put the database in.

If you did a lot of work and you did not provide a file name up front and you work in a version in which the .save command is not yet available (you quote that sqlite3 3.6.20 does not know it and I also do not see it in sqlite3 version 3.8.2) you can use the .backup command

sqlite> .help
[...]
.backup ?DB? FILE      Backup DB (default "main") to FILE

$ sqlite3
[...]
sqlite> create table mytable ( column1 text, column2 integer );
sqlite> insert into mytable values ( 'ENTRY1', 1 );  
sqlite> insert into mytable values ( 'ENTRY2', 2 ); 
sqlite> .backup main  temp.db
sqlite> .quit

$ sqlite3 temp.db
[...]
sqlite> .schema
CREATE TABLE mytable ( column1 text, column2 integer );
sqlite> select * from mytable;
column1     column2   
----------  ----------
ENTRY1      1         
ENTRY2      2