The sides of the court are named according to the score. When the score is forty-forty, it's referred to as "deuce." When playing a deuce point, the server serves from the right side of the court. Thus, the right side of the court is considered the deuce side.
When the score is ad-in or ad-out, the point is played from the left side of the court so that side is the ad side.
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An even number of points should have been decided when a serve is about to be delivered from the deuce court. In other words, all the odd number of 'points' should commence being decided via serving from the deuce court.
Therefore, for instance, the very 1st point being played in any one game is served from the deuce court. When that point is won by a player or team, an odd number of points will have been decided for that game. Therefore, the scores cannot be level when you move to serve from the Ad court. They can be even, however, when the serve is about to be delivered from the deuce court.
Thus when the ball is about to be served from the deuce court, the scoreboard must read as one of the following:
0-0 [Love all], or 0-30; 15-15 [called "15 all"], or 15-40; 30-30, or 30-0; 40-40 ["Deuce"] or 40-15.
More simply put, the scores must be level, or one side must be 2 points up when serving from the deuce court.
The deuce side of the court is generally considered the forehand side. However, that is based on right-handed players, so if a lefty is playing, their forehand will be on the ad side.