Visio can export a PDF file easily enough, but using a PDF as a design element in Visio is more complicated. Adobe's Portable Document Format isn't one of the file formats Visio can import or insert directly, so you need to convert the PDF file into a file format that Visio can use.
PDF and Visio Graphics Formats
It's simpler than it could have been because both Adobe's PDF and Visio's VSD file formats use the same underlying approach.
Video of the Day
There are two fundamental ways to create a graphics file: raster and vector graphics. Raster graphics save the image's pixels, while vector graphics instead save the image as a mathematical formula. You could think of it as the difference between putting a cooked meal in your fridge for later or just saving the recipe.
The PDF format and Visio's VSD are both vector-based, which makes conversions between the two more reliable than it otherwise would have been. Microsoft's general-purpose Windows Metafile (WMF) and Enhanced Metafile (EMF) graphics formats are also vector-based and can be used when Visio's own format isn't an option.
Using Word to Convert
Because Visio itself can't open a PDF, you need to use a program that can. One that's probably already on your system is Microsoft Word. There's no special process required to import a PDF into Word; you open it like any other file. Word can't edit a PDF directly, so it converts the PDF on the fly into an editable format without changing the underlying PDF. Then you can choose to export again as a PDF, or opt to save it in a different file format.
Choose Save As from the File tab, and then select either WMF or EMF as the file type. Better yet, save copies of the file in each format. There's always a bit of unpredictability involved in file conversions, so with any given file, you may find that one or the other does a better job of preserving the formatting and structure.
Use the usual File>Open command in Visio to open the EMF and WMF versions of the file in turn and see which one is more accurate.
PDF to Visio Native Format
Third-party software can provide reliable conversions, turning your PDF file into Visio's native file format (VSD) or something else it can read, including WMF and EMF formats and AutoCAD's SVG. There are several of those utilities, including PDFElement, pdf2picture and Insert PDF. Insert PDF is especially streamlined to use because it shows up as an option right on your Visio ribbon menu.
If you'd rather not download an additional program to your computer or if it's not permitted at your workplace, you can convert PDF to VSD online. Where VSD isn't an option, you can usually convert your PDF to WMF, EMF or SVG instead. Some sites provide an Application Programming Interface, or API, so you can automate the conversion process if you have the programming skills in-house.
Grouping and Ungrouping
Your newly converted PDF arrives in your Visio drawing as a single object, or shape. That's fine if you want to use the entire PDF as a single element, but more often, you'll want to separate its elements and use them individually. Right-click on the imported image and choose Group and then Ungroup from the menu that pops up.
Each of the newly ungrouped elements is still selected, so click somewhere outside the drawing area to unselect them before you do anything else.
Before you ungroup the elements in the PDF, take a moment to assess whether they're scaled appropriately for the rest of your drawing. If not, it's easier to resize them as a group than doing them all individually and trying to keep them to the same scale. If you have already ungrouped, select them all and reverse the process by right-clicking, choosing Group and then Group again.