There are some different possibilities to print PDFs... it depends whether you can require Adobe Reader to be installed (I don't know if you want to distribute your tool or just use it yourself).
1) It is possible to load the ActiveX control of Adobe Reader and use it for printing
pdfFile.src := 'filename.pdf';
pdfFile.LoadFile('filename.pdf');
pdfFile.print;
2) You can print PDFs with Adobe Reader itself (could be done with FoxIt too)
ShellExecute(0, 'open', 'acrord32', PChar('/p /h ' + FileName), nil, SW_HIDE);
3) You could also use Ghostview and Ghostprint
ShellExecute(Handle, 'open', 'gsprint.exe', PChar('"' + filename + '"'), '', SW_HIDE);
4) Or you could use a third party library... There are some available, but not all of them are free