It's difficult to find any direct materials online with references for America's Got Talent. From their official website:
DOES IT COST ANYTHING TO AUDITION?
Auditioning for America's Got Talent is completely free. Sure you still need to get to the venue, and maybe get a hotel for the night if it's a long drive, but we cannot reimburse you for your expenses. But if anyone is claiming they are with the show and want to charge you money to audition please contact us right away.If you make it beyond the first round of auditions, we will discuss with you in detail how we reimburse for travel arrangements as you progress in the competition.
So clearly once you actually get onto the show, there are some travel arrangements. I'll cheat a little in my answer here, and rather than give examples of America's Got Talent, I'll post some examples of information I found regarding American Idol, which will likely have a very similar expenses policy.
For American Idol, Fox Business describe the process for auditioning:
Auditions Can Be Expensive
...Audition costs remain a financial hurdle for hopefuls who follow the Idol audition trail from city to city, hoping to be selected.
"What the TV audience doesn't see is, if you're from San Diego and you audition and make it through in St. Louis, then you have to return to St. Louis a month or two later for the next round, and then again for a third round," says Rushfield. "Some can't afford to and drop out.
They then describe actually being a contestant:
Once chosen for the top 12, Idol contestants are provided room and board, although the accommodations have varied widely from season to season.
"There have been years where they want to show it on the air so they put them up in mansions in the Hollywood hills; other years, they've put them up in this apartment complex that's not seen on the air," says Rushfield. "It's nothing fancy, but it's not squalor. They have roommates all the way through, and when their roommates get cut, they consolidate them to save on the rooms."
A far bigger expense falls to the contestants' families. "They don't provide travel or expenses for families," he says. "That's the expense that causes the most trouble for Idols and their families."
What about costume expenses? The same article states:
Ever wonder whether Adam Lambert paid for those outrageous "Glambert" costumes he wore on the eigth season? The answer is yes -- and no.
"They go on a shopping trip with a fashion consultant who works on the show and they get like $450 a week to spend on whatever they want," says Rushfield. "But a lot of them dip into their own pocket because a few hundred dollars doesn't go that far in a lot of these expensive stores in Hollywood. The clothes are theirs to keep after the show."
As for how much they earn overall:
How much does an "Idol" finalist earn?
"Their payday for a year of very hard work comes to something like $1 million," says Rushfield. "The top four all do Disney World commercials; that's one of the biggest paydays. They also get money for albums and shooting the Ford commercials."
Then there's the show itself. The American Federation of Television and Radio Artists, or AFTRA, pays each top 24 contestant a performance fee: $1,571 plus meals for two-hour Idol shows, $1,303 for one-hour shows and $910 for half-hour results shows. But they all must fork over $1,600 to join AFTRA.
The biggest payday for most of the top 12 is the summer tour. "They get around $150,000 for four or five months of touring," says Rushfield.
The higher the finish, the larger the paycheck -- with notable exceptions. According to Forbes, season four winner Carrie Underwood led the pack, earning $13 million from June 2009 to May 2010. She was followed by season one winner Kelly Clarkson with $11.7 million. But Idol runners-up Chris Daughtry (third at $10.2 million), Kellie Pickler (fourth, $7.6 million) and Jennifer Hudson (sixth, $3.5 million) routinely out-earn winners David Cook, Taylor Hicks, Kris Allen and Ruben Studdard.
A different Fox Business article gives a more granular view of parts of the audition process:
Only a handful of contestants get called to audition for what the show calls "Hollywood Week." An "American Idol" insider confirmed that contestants are flown out to Los Angeles and housed at the show's expense. No meal money is given, but the shoot days are usually rather long and a contestant could easily eat all three meals for free while on set, according to the insider.
While Hollywood Week takes about five days to film, a contestant's time commitment varies. "They can stay the whole time if they do really well," says the insider. "Or, they can be done within a few hours on the first day."
If the contestant continues to impress the judges, he or she will be called back for live shows several months later. Again, the show pays for travel and lodging, but the commitment can last several weeks.
To confirm the overall amount earned by an Idol participant in a year, The American Idol Net.com fansite states:
ARE AMERICAN IDOL CONTESTANTS PAID FOR BEING IN THE COMPETITION?
Once a contestant reaches the Top 10 and in some seasons the Top 12, they start to receive a paycheck for appearing and performing on the weekly shows. At that point, they are also required to join the AFTRA union (The American Federation of Television and Radio Artists). The most recently reported hourly rate I could reliably source is $1,571.00 per two-hour episode and a bit less for a one-hour show. The Top 10 contestants (plus the wildcard pick this season) who go on to perform on the American Idol Summer Tour will also receive a fee of $1,000.00 per show.ARE THE FINALIST’S FAMILIES COMPENSATED FOR BEING IN THE AUDIENCE?
Even though American Idol loves to utilize the finalists’ friends and family sitting in the audience, either by airing reactions or actually bringing them up on stage, they do not compensate them for their expenses. The cost to the families can be quite high considering they must pay for travel and accommodations out of their own pockets. The audition process can also be a financial drain, considering some hopefuls must travel long distances to get to the audition city. If they make it through the first round they must travel back again to audition for the next round. These rounds of auditioning can be separated by several weeks. Many believe it’s well worth the expense for the chance to become an overnight success.DO THE CONTESTANT’S CHOOSE THEIR OWN WARDROBE AND WHO PAYS FOR IT?
The contestants are given a clothing allowance. The last verified amount I could find is $450.00 per week but it must be increased occasionally to keep up with inflation. A stylist, employed by Idol, accompanies contestants on shopping trips to help choose outfits for the coming week and advise them on what “look” will work best based on the their individual style as well as the style of their upcoming performance. Idol also provides them with a hair stylist and makeup artist.
So, I've given a bunch of articles and I'm well aware the majority of them aren't actually focused on your particular question - about America's Got Talent. However, I'm hoping they will still be of us considering the fact the shows are very similar and thus very likely have similar expense regulations.