What would be the best way to ask for $8,000 to get A 3D printer + supplies to make a prototype of an invention I have?
Consider saving costs by having your prototype printed by someone else's 3D printer instead. There are several ways to do this. Here are options in order of affordability:
1) Find local "hacker / maker spaces" (for instance check: https://wiki.hackerspaces.org/List_of_Hacker_Spaces) with a 3D printer. Either join, or make friends with a member(s) that's also interested in your idea.
2) Find a local 3D printing Meetup group.
3) Use 3Dhubs (https://www.3dhubs.com)
4) Use Shapeways (https://www.shapeways.com)
That might significantly reduce your expenses, which will make it easier for you to raise the money needed. To raise the money needed:
1) First describe your idea to friends and family. If they're interested mention that you're looking for early investors.
2) Consider applying to a startup accelerator which will give you both funding (sometimes up to $100k), and resources (many will have a 3D printer you could use, and other tools), as well as mentors and connections to investors.
3) Look into crowdfunding. This requires a decent amount of work, and many times you'll need to have already built some kind of prototype to get people to fund it.
If you'd like to discuss these possibilities in more detail, with respect to your specific idea, let me know,