Let's say we have a Cessna 150 or some other lightweight two seater and no chance to land with head wind for whatever reason. We're trying to land with a constant tailwind of 7 knots. I would try to land as close to stall speed as possible to compensate the tailwind. So much for the theory. In reality, the wind is not constant. If I'm close to stall, dying wind will give me trouble. What's a general good approach for such situations? What configuration would you choose? If the runway is very long, one can just go faster. But often, runways are rather short.
Land normally. Check your POH (Pilot Operating Handbook) first to ensure you have enough runway including the extra needed for a tailwind. The only thing to watch out for is that winds tend to moderate as you get closer to the ground. In a headwind landing, the relative wind will decrease, In a tailwind landing the relative wind will increase, so there will be an increased tendency to float way down the runway. Be on speed for a short field landing technique.
You should never try to land "as close to stall speed as possible".
Manufacturers have a recommended approach and landing speed for a reason. It is a compromise between a safe margin over stall speed, aircraft controllability, and landing distance. You should use their experience with the airplane by following their recommendations. Sometimes they have adjustments because of the wind, sometimes they don't because they don't feel that they are necessary.
Follow the recommended procedures and the POH/AFM will tell you the performance that you can expect. Do anything else and you are flying in an uncharted area (literally) and can find yourself in trouble.
Also, make sure that you check to see if there is a limitation for a maximum tailwind component for the specific airplane. If you exceed this, you can run into controlability issues or exceed the maximum speed that the tire is rated for.
In short, just fly by the book and be aware that you will use more runway so be sure to check the operating handbook to stay safe.
One thing that is an eye opener to people in regard to tailwind landings is when I ask them about wind gradients at low altitudes:
Wind is actually (supposed to be) measured about 10 meters above the runway. Because of surface friction that wind speed is going to decrease dramatically as you approach the runway surface. If that wind is a tailwind, as you approach the runway and flare your tailwind decreases and your indicated airspeed does what? increases, that's right.
So not only your ground speed is higher, but you just got a speed bump during your flare leading to a longer float.
The major problem with landing light aircraft, especially tail draggers with no steerable nose wheel,and tailwind component,is the lack of control when roll-out speed drops to that component or below. In fact,below it,control actions reverse! This is often more important than the higher touch-down speed, due to uncontrollable lateral departure from the runway,but at a relatively low ground speed.
It's not a huge problem if the wind is not too strong and there is plenty of runway. Ignore perceptions of groundspeed and land normally according to airspeed. I've conducted some experiments that actually tend to result in smoother landings with a tailwind component than with a headwind component; the wind gradient (which tends to increase or maintain the airspeed as you descend with a tailwind component) may be a significant factor in this. With a tailwheel aircraft, there is a risk of a groundloop as you slow down when landing with a tailwind. Don't do full-stop landings in a tailwheel aircraft with a tailwind if you can avoid it; a slight tailwind can often be tolerated for touch-and-goes. But a 7 mph tailwind should not be a problem for a Cessna 150 or similar tricycle-gear airplane if the runway is long enough and you use appropriate techniques.
Comments in other answers about the wind gradient tending to increase the float distance when landing downwind are definitely on target. Keeping the approach speed fairly close to the stall airspeed (e.g. 1.3 * Vso) will shorten your float and rollout distance. But definitely carry a bit of extra airspeed for safety if the wind is gusty rather than steady.
It's also worth noting that the wind gradient will decrease your climb rate on a go-around from a downwind landing, so the climb angle may initially be very poor.
Tailwind Landings are performed like any other landings. Bear in mind your groundspeeds will be higher than normal and you will have to anticipate higher rates of descent on final to maintain glidepath as well as a longer rollout once on the ground.
Performance wise, you will need to consult the airplane flight manual for the aircraft for short or confined field landing procedures as well as calculating landing distances. Do NOT attempt to land at or very close to the stall speed of the aircraft; follow the manufacturer recommended approach speeds Vref for your airplane and fly this plus a gust factor if needed on final. If an approach speed for short or confined fields is not listed for your light airplane, never fly final slower than 1.3*Vso + gust factor. You will need a small kinetic energy reserve in the roundout to arrest the rate of descent and place the airplane in the correct attitude for touchdown. If you are at or very close to Vso on final, you will not be able to arrest your descent without exceeding the critical angle of attack, resulting in a hard landing or potentially a crash.
Tailwinds do have the unpleasant side effect of greatly increasing the approach and landing roll; typically they tend to increase this by 10% for every 2 knots or so of tailwind as compared to landing in still air. Doubly unfortunate is that runways where there is no alternative but to make a tailwind landing tend to be one way in fields, often very short in length, with points of no return on approach. If these performance considerations are pushing up against the performance capability limits of the airplane and/or pilot, it would be wise to thoroughly evaluate this as part of your preflight risk management and select another day with more favorable winds to make the trip on.