This must be a naive question, but I have searched and just cannot find the answer.

I want to be able to crop and save a vector image (a graph) from a pdf file, later to be inserted into a latex file.

can inscape do this and what is the simplest way?

Well, you can try importing the pdf into inkscape and then:
- Draw a rectangle with the tool over the area you want to be visible
- Then, select the triangle with the tool
- Go to File -> Document Properties (Shift + Ctrl + D) and you'll see a button that says "Fit page to selection" in the 'custom size' area. Click on the button.
- Now, you can delete the rectangle, and you'll notice that the document border only covers the area you wanted to see.
- You can save this as pdf (or eps).

I'm not entirely sure if this works for saving as eps, but I've used it to crop and save as pdf (however I'm not entirely sure how latex handles these files, so it could be the it decides to ignore the page border). The region outside the border is still saved (so if you open up the pdf in inkscape, you'll still see the complete image, but if you open it in a pdf-viewer, you will only see the area inside the page border

Another method is importing the pdf into a raster editor (such as gimp), then cropping the image. Then import the image into inkscape and perform a Bitmap Trace over it.

Every format I've tried to saved the cropped image in always saves everything including the part I want deleted.

Why is it so difficult to crop anything in inkscape as compared to cropping in xv?

Welcome fulltlt!
Admitedly I don't know what kind of program "xv" is. But I'm guessing it's a raster graphics program. Although it probably doesn't matter, as far as answering your question.

There isn't a crop tool, feature or function in Inkscape. The proper way to crop in Inkscape is to use Clip, or in some cases, perhaps Path menu > Intersection. If you use Clip, it doesn't matter what format you want to save as, as long as you first save as SVG. Once you have an SVG version, you can save as anything you want, without any loss, afaik.

HTH