Welcome to the forum, Zach!
There are some plugins that attempt to do this inside of Sketchup - TIG's Image Trimmer and Thomthom's Bitmap to Mesh plugin are two of them. These can work, but I have found other methods to work better.
Cura Slicer will automatically make an STL from an image. You can then print the model directly, or save the STL and import it into Sketchup for further work.
Shapeways 2D to 3D utility will make a model. You can then download the model and convert to STL with Netfabb Basic for further work.
Convert the image to vector format using Illustrator or Inkscape, then save as DWG and import into Sketchup. This method usually makes the cleanest lines.
There are other methods you may find by searching "image to stl".
Hope that helps!