How to check if the column exists in sql table

A more concise version

IF COL_LENGTH('table_name','column_name') IS NULL
BEGIN
/* Column does not exist or caller does not have permission to view the object */
END
The point about permissions on viewing metadata applies to all answers not just this one.

Note that the first parameter table name to COL_LENGTH can be in one, two, or three part name format as required.

An example referencing a table in a different database is

COL_LENGTH('AdventureWorks2012.HumanResources.Department','ModifiedDate')
One difference with this answer compared to using the metadata views is that metadata functions such as COL_LENGTH always only return data about committed changes irrespective of the isolation level in effect.