What should I do to improve this bottle neck?

To get articles with ContributorID = null, make the join to the Sources table a LEFT JOIN.

You can look at the query plan in 2008, and it will suggest indexes but here are some starting ideas.

Users_Contributors (UserID, ContributorID) -- if USERID is always going to be 3 -- consider a filtered index that only contains rows where USERID = 3.

Articles (UserID, SourceID, ContributorID) -- same comments about filtered index

Sources (SourceID, Name)

By the way, how is join at the bottom supposed to work? What column in the contributors table itself are you joining to? Assuming you meant Contributors.ContributorID instead of Sources.SourceID, then

Contributors (ContributorID, Name)

Never cut and past bits and pieces. You should always show the code that is actually running as a whole. A join to a table that references no column in that table makes no sense.

Inner Join CONTRIBUTORS On Articles.ContributorId = Sources.SourceID

In terms of the paging i would point you here.
Are you able to post the actual query plan for the query ?

If you need all columns of ARTICLES matching or not CONTRIBUTORS, then use a LEFT JOIN instead of INNER JOIN. Use the same rule for ARTICLES if it applies.

The first performance tip i can give is to replace your IN() by EXISTS or even LEFT JOINS:

-- replacing IN() by LEFT JOINS
Select Articles.ArticleID, Articles.ContributorId, Contributors.Name, 
    Sources.Name, Articles.ArticleTitle
From Articles 
                LEFT JOIN Contributors On Articles.ContributorId = Sources.SourceID
                LEFT JOIN Sources On Articles.SourceId = Sources.SourceID                      
    			LEFT JOIN Users_Contributors On Articles.ContributorId = Users_Contributors.ContributorId AND Users_Contributors.UserID = 3
    			LEFT JOIN Users_Sources On Articles.SourceId = Users_Sources.SourceId AND Users_Sources.UserID = 3
Where   Users_Contributors.ContributorId IS NOT NULL
    	OR 
    	( Users_Sources.SourceId IS NOT NULL AND Articles.ContributorId is null )

-- replacing IN() by EXISTS
Select  Articles.ArticleID, Articles.ContributorId, Contributors.Name, 
    	Sources.Name, Articles.ArticleTitle
From    Articles 
                LEFT Join Contributors On Articles.ContributorId = Sources.SourceID
                LEFT Join Sources On Articles.SourceId = Sources.SourceID                      
Where EXISTS
    (
    Select top 1 1 from Users_Contributors
    Where UserID = 3 AND Articles.ContributorId = Users_Contributors.ContributorId
    )
    OR EXISTS ( Select top 1 1  from Users_Sources
                Where UserID = 3 AND Articles.SourceId = Users_Sources.SourceId
                )
                AND
                Articles.ContributorId is null
    )

Basic Indexes should be all ids with clustered index, nonclustered index on Users_Contributors( ContributorId, UserID) and Users_Sources( SourceId, UserID ).

For paging, i would suggest row_numer() function, its something like:

with aux(
    Select	row_number() over( order by <some order criteria> ) as id,
    .
    . <remaining select>
    .
)
select * from aux where ID between @start_value and @final_value

Let me know if this helps...