When faced with a strong color, neutrals will always match it. For instance, a green of any shade will always go fine with white, black or gray. White is the classic choice. A cool gray to pick up cool undertones in the green is a winner, too. Black is a brassier choice. It can be stark, but depending on yard hues and your taste it can be a good choice for trim. For siding, it will be too powerful.
Match subdued siding shades, which will cover the majority of the skin of the house, with a more pronounced trim color as a way to add hue without the house color becoming blaring. For instance, taupe siding, or simple white gives you a neutral base. Add to that a color the hits it off with the green. Turquoise, moss or a lighter green shade are all colors that harmonize.
The other option is to go for a more intense siding shade and keep the trim color neutral. For this, barn red on the siding is colorful, but has enough restraint to be tasteful. The red and green, as complements, create a strong color impression. Historic colors such as Nantucket blue are good choices, too, as historic colors are dampened down a bit with a little neutral admixture. For trim, stick with grays, browns or white.
If you want to make a statement, ratchet up the color by using high-impact hues on trim and siding. There are two color options that are standard harmonies. The triadic color harmony matches the green with two other colors equidistant on the color wheel, in this case orange and purple. Use one on the trim and one for siding, and consider pastel versions to soften the shades. Split complement harmony takes the hues on either side of your complementary color, red. Here, use red-orange and red-violet hues to complete this home color harmony.