You'd probably be wealthy enough to have a horse for the journey, and more horses or ponies for each of your entourage (who would probably be slaves acting as bodyguards). In principle you could go on foot, but if you were poor enough that that was necessary you might well not be able to afford the consultation itself.

You'd need enough money to sustain yourself along the way, in whatever the most widely circulating currency of the time was (e.g. Athenian or Aiginetan coins in the earlier period), enough travel gear for the 120 km journey each way, and emergency supplies in case you couldn't buy your necessaries in any given day. Most of the classical Athenian diet consisted of grain, though, so your food agenda would probably revolve around a large supply of that and making yourself a bland barley soup most days (yuck).

Once you got close to Delphi the process would be made easier by the fact that everyone would be in consultation-day mode. There'd be a crowd of people converging on Delphi, because the oracle seems to have operated on only nine days in the year (one day in each of the months that Apollo was supposed to be residing in Delphi). It wouldn't be very unkind to suggest that it was basically "screw over the visitors" day.

Once you were actually there you'd need money for the following procedures:

1. hire a Delphian sponsor, because non-citizens in ancient Greece generally were not permitted to use local cult apparatus unless accompanied by a citizen;
2. acquire a goat for the sacrifice that served as the entry procedure; it's likely that this would be obtained from the staff of the oracle itself, as that would simplify their economical position (and at a stiff mark-up);
3. hire a priest to sacrifice the goat in front of the temple.

Then you could go and consult the Pythia. (There were two priestesses on alternating duty at any given time, with a third in reserve.) Your answer would normally be a straightforward "yes" or "no".

Further reading:

• Bowden, H. 2005. Classical Athens and the Delphic oracle: Divination and Democracy. Cambridge. 12-39.
• Eidinow, E. 2007. Oracles, Curses, and Risk among the Ancient Greeks. Oxford. 42-55.