In order to take advantage of business and first class international seats, you have to build up some pretty large stores of miles and points to make use of. There are a number of ways to do so, but none are quite as lucrative as credit cards.
Opening and closing credit cards can grab you huge swaths of points and miles all at once. This is a strategy that must be planned out, and executed with care though. Losing control of your spending on credit cards can not only put you in debt, but leave you paying massive interest rates that immediately negate the points you earned in the first place. The aim is to pay off your card every month, and never ever see an interest charge or any other type of charge.
When I first started doing this last year, it was easy to make work. There were some rules that had been put in place by credit card companies as they try to make it harder for people like us to move credit cards around in our wallets like a mad man. Opening and closing cards for points and miles is referred to as credit card churning. Credit card companies in the last few months have begun to implement even further restrictions on opening cards.
Chase has a 5/24 rule, Citi has a new rule on opening types of cards, and Amex has the famous once per lifetime bonus restriction. If you know these rules though, you can work around them and change your habits to better work with credit cards and gain many points.
Keeping an eye on your credit is very important as well. Credit bureaus will have you believe that opening many cards will negatively impact your credit. This is partly true, but the additional credit that is opened up for you on the new card is weighted much higher than the negative impact of the credit lookup. This means that getting credit from a new card will in most cases increase your credit score, not drop it. Keep that balance at $0 though, otherwise it will negatively impact you with interest charges, and drop your credit rating. Use services like Credit Karma to track your credit score for free and keep on top of any negative changes.
This is also a game to be played by those who already have pretty good credit. Getting approved for these cards in many cases requires good credit.
Always track everything. Nothing got me tracking my spending quite like jumping into this churning hobby. Track the dates your were approved so you know when to cancel if you don't want to pay the yearly fees, or when the yearly fee is due if you want to keep the card. Track the money spent on each card. Track if this card can be reapplied for and when. These are very important things to remember in churning. All of this will lead to large points/miles stores that will allow you to take some amazing trips for next to nothing out of pocket.