Both the ancient site and the new town of Delphi are right on the mountainside and therefor very steep.
So take your time when you are there and don't rush as you might just slip and fall.
And try to put on some good footwear when you are in Delphi as you don't wanna ruin your trip with a foot injury.
Don't even think about touching anything. The guards will flock to you and watch you like a hawk the rest of your stay at the ruins. They WILL kick people out, too. Just ask 2 of the people who were on my bus.
Watch out for the marble. I had this problem all over Greece. Marble is beautiful, but it is not the easiest surface to walk on. While walking through modern Delphi in my flip flops, I almost fell at least 10 times. The leather sandals I bought prooved to be much better suited to the slippery marble. My advice: wear shoes with a good sole, and don't wear flip flops unless you have no other choice...in that case, walk on the cement between the blocks.
Just a warning to those people who are not in shape, or those who think they were, but who really were not (me), be forewarned about the ascent to the stadium. I was there and it was stifilingly hot (my excuse). It was tedious, but very worth the effort to reach the top and roam around the stadium.
It's not a great danger but just a warning for all folks thinking that Delphi is a flat sanctuary. You're all wrong!!!
Be sure that you will need all your energy to climb this sanctuary !! And don't forget that the stadium is on the top of the sanctuary.
Make sure you got some good walking shoes and bring a bottle of water.