I started doing this 7 years ago so I've built a really decent credit history. Here's how I did it (quite masterful btw),
The Continental Onepass credit card was about to expire with a 50K offer (Because of the United merger), so I applied for on the last day at the same time with the United MileagePlus version with a 50k offer. I was of course denied for both, but NEVER GIVE UP. Call the Chase reconsideration number and tell them your reason (mine was I needed both a Mastercard and Visa due to traveling a lot). Also I registered a brand new Continental Onepass number because they say you can only get one bonus offer per frequent flyer number, but this gets around that (you can later merge accounts, so no big deal). Then 55K offers + $50 statement credit came out right after, so I sent a secure message for them to switch me to that offer (you can upgrade offers within the first 90 days of card opening)
Then 32 days later (you have to wait 30 days between chase apps), I applied for 3 more Chase cards at the same time (3 different browers so it only gives you 1 credit inquiry). This was really risky because it looks like i'm desperate for credit, but i have a great history with Chase. I could only convince them to accept me for the Chase Sapphire Preferred and Chase Ink Bold Biz card, which were the cards I really wanted anyway (denied for Chase Freedom). Sapphire offered 50K Ultimate Reward and Ink Bold offered 50K (upgraded to 60K with secure message). These are tougher because you need spend 3K for sapphire and 5K for Ink Bold to meet minimum spending requirement. These cards took some REAL smooth talking because the United/Continental credit cards a month earlier. I told them I made a huge mistake and didn't know that Ultimate Rewards actually transfers to United Airlines on a 1 on 1 basis making these cards way better than the previous cards.
This may be a bit overwhelming. The same offers aren't around right now, it's ALWAYS changing. It looks like they are toughening up on offers, but you can at least get the United card, Sapphire, and Ink Bold and simply ask them to upgrade your offer via secure message after you get the card. It really works.
While I tried to explain everything I could of what I did, you really need to hang out at these 4 websites to get a real hang of it:
http://dansdeals.com (check out his forum too)
http://flyertalk.com (read their MilesBuzz forum)
It took me 7 years to become a Jedi Master at this stuff, so have patience. If you have little credit history. Pick just one card from each major company and wait a year. Also if you have parents or friends who long credit histories on an personal American Express card, beg them to put you as an additional user so you suddenly get ALL of their history for that card which will really extend your average account age. Also, check out your credit score all at the out for FREE at http://creditkarma.com. Super awesome site!!!
Hope this helps. Feel free to ask me any question you have.