you've different options
1. use a string parsing UDF and get the array returned as a table of values and use it in join to do filtering
so in your case
SELECT...
FROM...
...your rest of the query
INNER JOIN dbo.ParseValues('first,second,third',',')f
ON f.Val = Yourtable.Field
ParseValues can be found in below link
http://visakhm.blogspot.in/2010/02/parsing-delimited-string.html
2. Use string based comparison like
DECLARE @FilterList varchar(8000)
SET @FiletrList = 'First,Second,Third'
SELECT...
...
rest of query
WHERE ',' + @FilterList + ',' LIKE '%,' + YourTablefield + ',%'
there are few other methods also like XML method which is discussed in below link
http://vyaskn.tripod.com/passing_arrays_to_stored_procedures.htm
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SQL Server MVP
http://visakhm.blogspot.com/