You should start by developing a checklist from your project specificaitons regarding vendor supplied materials.

All good responses above-

As Goose mentioned the list can go on and on-

As far as the specific visit-
I would suggest you contact the vendor ahead of time and discuss the purpose of your visit and make an appointment with the correct contact individual there (i.e. quality manager, manufacturing superintendent, etc,) .  Advise him your arrival time and est. time to complete the visit.  Ask for any required shop safety equipment, (hard hat, safety glasses, steel toe, etc. and BRING YOUR OWN.)  Arrive on time!  Have an opening meeting to discuss how basically you would like your visit will go  (i.e. shop tour, meet with QA manager for document review, welder certification, calibration documents (don't forget lunch break)  processes review, blasting procedures, painting shop, etc).

Send a written plan/checklist ahead of time, so the guy can be prepared and knows what to expect from you.  The last thing he wants is surprize requests that takes time to locate or compile, and you really do not want to may make him look bad in front of his employer.  You are there to develop a professional working relationship with this vendor.  If he has what you need he'll get it, and if he doesn't, he may advise you ahead of time. 

Do not stray, and work off your checklist - but be flexible when you get there.

Make good notes, but don't ask for document copies unless really required.  I mean ..Do you really need a copy of Eddie Sparks welder certs at this time?

Try not to interupt any work in progress in the shop

Do not criticize peoples efforts

Have a closing meeting to discuss your findings, compliments, compliances, non-compliances, etc... at that time provide a written list if any required action items are still needed from the supplier.   Keep an eye on your watch and try not to overstay your estimated time to complete, and thank them for their time.  Take good notes and write your report as soon as possible.

THIS MAY SOUND STUPID but this is what can happen without a plan:
Richard the inspector phones and says he will be here Tuesday morning.  He finally arrives at 9:20 am.  We walk into my office where he drops his briefcase.
I ask, "where would you like to start?"  He says "up to you".  I say, How about a tour?  "OK" he says.  I scramble to find him a half-way clean hard hat, some safety goggles that will fit over his prescription glasses, and tell him to stay in the yellow lines because he doesn't have steel toe shoes.

We tour the facility.  Richard talks about the packer game mostly and how much money he lost on a bet.  I introduce him to the weld shop foreman, and show him our weld shop, and welder certification booth...he just nods.  I show him our NDT office, we meet the NDT guy who describes our capabilites, he shows him the equipment.  We meet the lead man in the paint booth, etc. etc.

We return to the office.  Richard sits down opens his notebook and asks, "can I see your welder certs?"  We stand, return to the shop, back to the foremans office where we were 45 minutes ago, and he show him the certs.  We return to the office where his notebook is.  He writes someting in the book.  Then he says, "can I see your NDT equipment calibration reports?"  We return back to the shop NDT office, interrupt my inspector again...and then show him the docs and cal stickers he wants.  Back to the office.  "Can I see your NDT inspectors level II certification?" is his next request.  I tell Richard that the certs are back in the inspectors office where we just came from...but it is hard to hear because my teeth are clenched soo tight and smoke is coming out of my ears... 

anyway-
(Don't be a Dick, I mean Richard.)