Assuming that you want to do it properly, that is you want to replace meat with various vegetables, nuts, and beans etc that provide protein you automatically increase your intake of healthy foods.
You can of course just eat chips, cheese and margerita pizza which won't help. But being vegetarian does open your eyes to a wider variety of food than just meat + x (e,g. buger + fries). Meat is so tasty on it's own that you can ignore other things.
By going vegetarian I don't have to count calories, I've actually struggled to keep weight on since going full vegetarian, when I had been gaining weight prior to that.
Plus you don't even have to go fully vegetarian, purely just reduce meat intake and up vegetable/bean/nut intake.