Don't Starve Guide: Bait seagulls with mushrooms
Well, I recently discovered this cheap way of farming seagull. This method costs almost nothing but some bird traps, as your mushroom don't get eaten.
It becomes pretty handy when you have some useless mushrooms (like the red ones, or all mushrooms when you play as Maxwell).
Note that this can only be done during Hurricane season. One big trouble with this is that mushrooms do get blown away by strong wind, as you can see in the video... So this might not be the best way, but definitely one of the least costly ways to capture a seagull!