If your starting point is the Moon (Luna), it is always better to drop to LEO altitude and perform a second burn there to get to your destination. The more the transfer Delta-V (Total DV in TransX or oV in IMFD), the more the savings compared to leaving directly from the Moon.
For a direct flight, the best tool to use is IMFD.
www.youtube.com/watch?v=i2iB3CXirVk
The two burns method can be setup only with TransX. There are a couple of ways to do it, (surrogate ship or 2 instances of TransX). For more accuracy, you can handle the burns themselves using IMFD's Delta Velocity and Map programs.
This link from flytandem is very useful for making a plan with a surrogate ship in TransX.
This post from BrianJ is for making a Moon to Mars TransX plan without the help of a surrogate ship. The starting point is from lunar orbit.
These excellent videos from David Courtney, walk you through the process of setting up the flight with TransX from the lunar surface. Very highly recommended.
www.youtube.com/watch?v=Zk8-nPBtYeY
www.youtube.com/watch?v=p0KubAYmD_Q
(more examples to be uploaded soon).
One small technical detail. It is not a sling, not even a powered slingshot. For a trajectory to be considered a slingshot, you need to enter the system with a hyperbolic trajectory. In this case you -standing on the Moon- are already in an elliptical orbit around the Earth. It is just a 2 burns method to leave the Earth-Moon system. One burn to leave the Moon and drop to a low altitude over Earth and a second burn there to escape the Earth.
There is also a third way to make these flights (moon→other planet), which is a 3 burns method.
1.You leave the moon and go to a high apoapsis relative to the parent planet.
2.At apoapsis you lower your periapsis as close to the planet as you can. (And take care of any plane change needed)
3. At periapsis you perform the ejection burn.
Not really applicable in the Earth-Moon system, but it's a really useful method if you are landed on a moon of the outer planets. (IIRC, it even works for Deimos-Mars). The down-side is the additional flight-time.
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