I am traveling to Hungary for first time our flight is Detroit to Amsterdam to Hungary. Will I need to go thru customs in both Hungary and Amsterdam? And how much time do I need to allow in each area.
You will go through Immigration(passport control) in Amsterdam lines can be up to 30 minutes. There is often an express lines available for people with tight connections; there will be a monitor overhead listing which flights qualify. Customs (the stuff your are carting with you) will be in Budapest, but this is usually just a walk through non-event.
Unless you need to declare that you're carrying more than $10,000 cash, or other items of peak concern to customs agents, then you don't even talk to them.
In literally dozens and dozens of trips to Hungary I have only on a very few occasions seen anyone at the customs table. I can only think of once when I saw someone having a bag inspected. If you have something to declare you actually have to track someone down to do it.
Amsterdam is a pretty decent place to change flights. I have had only one experience where the line was long and time short. We ran and made it just the same. But that was one in about 8 changes in Amsterdam.
When you get to Budapest, get your bag, look for the sign that says nothing to declare. Go through the nondescript black glass door and you will find yourself in the Arrivals Hall. Continue walking straight (past all the private taxi drivers hawking their services) and in about 40 feet you will find the doors out. To your left and about another 40 feet you will see the Fotaxi Kiosk. Tell them where you are going, they give you a slip of paper and you move about 30 feet to the first cab in line where someone will help you with your bags and open the car door for you. Give the driver the slip of paper and 30 minutes and $35 dollars later more or less you will be in the center of Budapest. I have been a lot of places and few are this easy and this cheap.