How to do a slingshot maneuver

[I likeOxidizerrfuel]

Hi creators! My question for today is, how to make a slingshot maneuver because I want to save fuel to go to Duna. Any ideas how? Also, include an image if possible with you answer. Thanks!

Edited August 11, 2019 by I likeOxidizerrfuel
I made a typing error.

[Gargamel]

Moved to Gameplay Questions. 

[bewing]

If you wait for your Duna window, and then wait a few days more for the Mün to line up properly, then you can do a slingshot like this and save a few hundred m/s of dV.

[IncongruousGoat]

The short answer is "a lot of messing around with maneuver nodes and timewarping".

The long(er) answer is as follows (and note that this applies to any use of assists, not just this one):

1. Work out what body you want to assist off of. Good candidates have deep gravity wells and are "closer" (in delta-V terms) than wherever you're going. Eve, for example, is a popular target for missions heading to the outer solar system, since it's big and easy to get to from Kerbin. In your case, however, the only reasonable choice is the Mun, since it's the biggest body that's "closer" to you than Duna.

2. Set up a transfer to the target body.

3. Tweak the transfer until the orbit you'll end up in after the flyby looks good. "Looking good" in this case can mean any number of things, but in general means either A: encounters (or get close to an encounter with) the target body, or B: if that's not possible, at least ends up crossing the orbit of the target body. In case B, you'll end up needing to wait a few orbits for an encounter to happen.

These rules apply to any gravity assist in general, but there are some specific transfer routes that have been found to work reliably without too much waiting around. The Mun->Duna transfer has already been explained in this thread, but also worth mentioning is the K->E->K->K->J transfer, which is highly reliable and ever popular for missions to Jool. A full explanation of how that one works is a bit off topic, but I'm sure you can find several threads where it's been explained to death.