Ok, here is a small tutorial to use a gravity assist with Venus to go to Mercury.
First, send your ship on LEO, then aim for Venus. Here is my predicted burn:
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You can notice that my trajectory goes quite below Venus level at its periapsis. This is intentional, and this is important for what will follow. If you use a cheaper transfer, the gravity assist that will follow won't be powerful enough.
After I performed my burn, my trajectory is the following:
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I planned a low fly-by above Venus. Which is important here is to pass in front of the planet. Making the fly-by on the other side would make you go higher on the contrary (which can be used in a different technique to go to Jupiter and above).
Here is my ship before the encounter:
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That way, Venus deflects my trajectory backwards, which is what I need here.
Once I entered Venus' SOI, I can see my exit trajectory:
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Voila, I'm on my way to Mercury
You can eventually tweak the height of your fly-by to adjust your trajectory. The periapsis of your Sun orbit should be as close to Mercury as possible (ideally, just slightly below). This is to minimize the cost of your insertion burn.
Now here comes the tedious part, I have to wait for a cheap encounter. Aim for Mercury, and wait for the game to propose you a cheap burn. Try to spend less than 50 m/s, and if possible favor a retrograde burn.
I had to spend 45 m/s for this:
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Now I have my encounter with Mercury, I can perform my injection, and it's over:
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I made a quick calculation, it allowed me to save around 600m/s (by taking into account the burn to get the encounter). This is quite an interesting discount compared to the 2784 m/s you need with a direct transfer. I know you're not really into numbers, but that gives you an idea about what you gain
Of course, you can do something similar when returning from Mercury: aim for Venus, and a new gravity assist will send you directly towards Earth.
Last advice, don't forget to make a quicksave because it's easy to mess a gravity assist at first.