How good of a guess do you need? If you want something that's +/- 50% you can probably do that pretty easily. +/- 10% is probably impossible at this stage. They will do a roadshow (fly around the country literally pitching large investors on buying their stock). After the roadshow they will gather data about the interest, and where it's from. Institutional investors are usually preferred over retail because they are less likely to immediately flip the shares -- but institutions may not pay as much. They will hope to have far more interest than they have shares allocated for the IPO, which will allow them to raise the price (stokes interest in the stock, which helps support the price once they're public). There's a lot that goes into this and I'm only marginally more knowledgeable than you are, so I'm probably missing 90% of the interesting stuff.

If you are a shareholder and asking from that perspective, or know any employees who may hold options, you should keep in mind that there will be an associated lockup for 180 days after IPO, during which time the stock will probably do all sorts of "interesting" things. Predicting the price it will be when the lockup expires is beyond anyone's ability. :)

Down the line there will be estimates -- companies progressively update their S-1s as they approach the actual IPO date. It's almost always challenging to get in at the opening price, though -- usually those are deals done with big funds and banks that help place shares.