If your plane has less maneuverability than the opponent's

[Phoenix]

This is something I struggle with, but what do you do in that case? All I've got is to do a few low yo-yo's, and that does not always work.

[Bombcat]

The solution here comes from two angles - first, you need to play up your relative strengths, and second, you need substantial skill. There are some cases where it would be unreasonable to expect success. If, for instance, you are in a stock F-14 Tomcat, and your opponent is in a stock F-16, your chances of winning a close turning fight are very low unless your opponent is much less skilled. The stock Tomcat offers no significant performance advantages in a close fight, and so you would rely entirely on capitalizing on your foe's failures to properly use his machine.

Moving onto a more manageable fight, let us say you are in a stock F-100, flying against a stock Su-27. You will lose a turning fight, more likely then not. You have a vast superiority in firepower, however - all you need to do is get your nose on him once, possibly in a head to head pass, and you can rather quickly shred his plane.

Another possibly example: in a fight between a 171st Tomcat and a stock or 171st A-4 - the A-4 has a major turn performance advantage, but the Tomcat is much faster, and can more easily engage in high speed vertical maneuvers. The A-4 will focus on a slow, turning fight to force the Tomcat in front of it's guns, while the Tomcat will make several high speed passes, relying on speed, and the pilot's shooting skill, to get a kill with minimal risk.

To sum up: There is no one right way to beat a more agile opponent. Look for openings (a bad turn, a poorly executed stall), take advantage of any performance advantages you have (speed, firepower), and recognize when it is not wise to engage. I'd need specific information on the two planes involved to recommend specific maneuvers or tactics.

[Animal]

If your airplane has a slower turn rate, but tighter radius, try horizontal scissors.

[Midnight Rambler]

... I'd need specific information on the two planes involved to recommend specific maneuvers or tactics.

Sopwith Camel VS. Stock F-16

[Phoenix]

Thanks Bombcat, Animal.

In terms of specific aircraft: TF58's (I think) Mirage3 and Mig 21, or stock F-4 and Mig-21