In nearly every case, when you book an outfitted hunting adventure, the cost of licenses IS NOT included in the price of the hunt. The hunters are required to acquire licenses from the state and any additional jurisdictions, and to pay for them. However, in some cases the state licenses are acquired from or through the outfitter especially in places where there are "outfitter allocations" of tags.
In places where a nonresident hunter is required to enlist the services of a licensed guide/outfitter to hunt certain species, you'll need proof that you've hired an outfitter before you can acquire your license. That can be your contract with the outfitter, or in some states, provinces, and countries there is an actual government document that needs to be completed by both the outfitter and the hunter(s) to submit to acquire the license.
Your primary source of information on applying for or buying licenses should be your reputable, trustworthy outfitter. His/her willingness and ability to help you through the sometimes complicated licensing process is another strong indicator of reputability of the operation. A reputable outfitter wants to ensure that you have the correct license and will do all he/she can to help you acquire it. If you find yourself working with someone who doesn't seem to care much about licensing and legal aspects of the hunt, you'll want to reconsider booking/hunting with him/her.
An experienced, highly-rated outfitter can be an excellent source of information when it comes to applying for limited draw licenses. They know areas with great animals, that might be too tough for unguided hunters to access or that are often overlooked for some other reason. Their tips can help up your odds of drawing a great tag.
While the outfitter should be willing to help you get the appropriate licenses, the bottom line responsibility of making certain you get all the right licenses for the right location is yours. If something went wrong and you were to face charges of not being properly licensed, it's you who would face prosecution and penalties, not the outfitter.