Is there a need to appear before the beit din? If so, it would seem to make sense to find a beit din locally to avoid travel expenses.
The best way is for both spouses to appear before a beit din. (If necessary, or the couple can't stand to be in the same room, then the husband can appear before one beit din and arrange for a proxy to deliver the Get to his wife.)
Most Orthodox rabbis in most Jewish cities can usually arrange for a beit din with the right expertise to travel in to the necessary city. (Though it may take some time to schedule that.)
Is there a set price, or does it vary by beit din? What might the cost be and is there a way to keep the cost down?
It can vary, but it's basically the cost of the time of the experts. Anything more than a few hundred dollars is wrong. A competent beit din should never refuse someone who's truly unable to pay.
After the ritual "you are no longer married" ceremony is over, a beit din can then, if the couple chooses, hear a civil case to determine the division of property and child custody. The longer that takes, the more expensive that will be. But if they just stick with the ritual ceremony, basically if no one tries to bog things down, it should be quick and cheap.
What documents will a beit din ask for?
There are only three variables in a Gett: the husband's name (including his father), the wife's name (including her father), and the name of the city where the Gett is being transacted. How to properly spell the city is the rabbi's job. So all they need is "how do you spell your Hebrew name? Your English name? Your father's name? Are there any other names or nicknames by which you go?" If the couple has a document like a ketubah, that can be helpful to ascertain some spellings of names. But generally, just think about the Hebrew names in advance and that should be all that's necessary.
How long will the process take, from beginning to end, assuming no unusual circumstances.
In Israel, the bureaucracy books them in 45-minute slots. Most other places allow 90 minutes to give people a bit more time.
How does one locate a beit din to use for a Get?
Top-down: Email [email protected] . The Beth Din of America (in NYC) will probably know who to call. Bottom-up: most local Orthodox rabbis should know who to contact. (But once they give you a name, by all means do double-check it with bethdin.org to make sure it's someone reputable.)
What other practicalities come to mind?
There is nothing in a Gett about why they're getting divorced, whose fault it is, anything like that. The beit din will usually start off ascertaining that all hopes for reconciliation have failed, and should push no further. (Note: if the husband is a kohen, the process becomes more complicated as they'd be prohibited from remarrying.) If the couple can be civil to one another through the process, there's no reason for it to be antagonistic.
The biggest suggestion in recent times concerns the wife: the typical Gett procedure will involve easily half a dozen men in the room, whereas the only woman required to be there is the wife. Even if everyone is trying to be understanding and helpful, that gender imbalance can feel awkward. There is no reason why she can't bring a friend or two for moral support, and in fact many beit dins encourage it today. (Note: "moral support" does not mean yelling at the rabbis.)
