If you are looking to get some credit for the very first time, lenders can't take a look at your FICO score to see if they want to lend you money. When this happens they have to evaluate other factors to help them decide if you are a credit "risk" or not.
One of the first things they look at is employment history. Lenders need to see if you can hold down a job or if you've had periods of unemployment. Your ability to keep a steady job will augment the chances of getting approved.
Lenders also look at residence history. They can look at how often you move or if you rent or own. Just the same as employment history, it is really good to have a stable residence. Owning a home, even if jointly with a partner, carries loads of weight as well.
Having utilities in your name is also good; it shows your "purchasing power" and ability to pay bills over time steadily. Without a credit history you can still pay for many utilities in your own name. An electric or gas bill, telephone, cable, or water service in your name is perfect. Having your name alone on these accounts won't give you a credit score, but it sure is helpful for first-time borrowers.
You must have been shopping at a mall once and been asked if you wanted to apply up for their store credit card to save 20% on all your future purchases. Most of the time, store cards are a bad idea. They entice you with an immediate discount and promise of future savings, but they also have high ongoing interest rates.
Usually you should avoid these cards, but they are very easy to obtain and immediately start to earn you credit worthiness. If the local bank didn't work out, you should consider getting a local department store card. It's very important before you apply to make they report to the credit bureaus, otherwise all your credit worthiness earning will be for nothing.
Once you get a "mall card", you should be disciplined and use it with respect. Remember, this is your last chance at earning back credit worthiness. Use it only to earn credit worthiness and not as an actual credit card. Only buy with it if you know you could buy with it anyways on the spot. Then promptly pay it off so as to gain credit and have it reported to the credit bureaus. The limit will almost surely be low anyway. It is very important to keep paying the bills frequently and regularly so your credit history can be built upon it.
Establishing good credit worthiness takes time. You cannot take shortcuts or use tricks to circumvent the system and get you a high score in a matter of months. It is important to get your first credit, it is even more crucial do the right things to keep that good credit.