SQL SERVER: How can we find whether a table is existing in our database or not?

Use pubs
select * from information_schema.tables -- to get details about all tables.
select * from information_schema.columns -- to get columns of all tables.

Most of the DBA level info can be extracted from information_schema views.
Some more format:-
View Name Description
CHECK_CONSTRAINTS Holds information about constraints in the database
COLUMN_DOMAIN_USAGE Identifies which columns in which tables are user-defined datatypes
COLUMN_PRIVILEGES Has one row for each column level permission granted to or by the current user
COLUMNS Lists one row for each column in each table or view in the database
CONSTRAINT_COLUMN_USAGE Lists one row for each column that has a constraint defined on it
CONSTRAINT_TABLE_USAGE Lists one row for each table that has a constraint defined on it
DOMAIN_CONSTRAINTS Lists the user-defined datatypes that have rules bound to them
DOMAINS Lists the user-defined datatypes
KEY_COLUMN_USAGE Lists one row for each column that's defined as a key
PARAMETERS Lists one row for each parameter in a stored procedure or user-defined function
REFERENTIAL_CONSTRAINTS Lists one row for each foreign constraint
ROUTINES Lists one row for each stored procedure or user-defined function
ROUTINE_COLUMNS Contains one row for each column returned by any table-valued functions
SCHEMATA Contains one row for each database
TABLE_CONSTRAINTS Lists one row for each constraint defined in the current database
TABLE_PRIVILEGES Has one row for each table level permission granted to or by the current user
TABLES Lists one row for each table or view in the current database
VIEW_COLUMN_USAGE Lists one row for each column in a view including the base table of the column where possible
VIEW_TABLE_USAGE Lists one row for each table used in a view
VIEWS Lists one row for each view




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