Your ability to hold two full-time jobs depends on the rules and contract of your first job. Holding down two full-time jobs requires a lot of stamina, focus and caution in managing the needs of two jobs and two bosses. Never put yourself in a situation where you could stand to lose both jobs, because you need to keep at least one. In most situations, it is legal to hold a second job, but it can still be cause to get fired if you can't do the first job to the level expected of you.
Review your employee handbook. When you took your first job, no matter what it was, you should have been provided with some kind of contract, employee guidelines or handbook outlining the rules, requirements, bylaws and commitments required of you. Some employers will explicitly state that a second job cannot be held in tandem with the existing job (this is legal, particularly if the job affects the public safety, such as airline pilots or doctors). Most often it is legal to hold a second job, but your employer's rules will state that any second job attained cannot be in conflict with the first, and you can be fired for cause if you breach that code. This means you cannot work for a competing company in that same industry or in anything which requires hours that conflict with the requirements of your first job.
Narrow your job search for second jobs to only those that do not conflict with the needs of your first. It is best to be honest when applying that this is a second job for you, as any information you have kept secret that comes out later can get you fired from your second job. In addition to the regular working hours, be clear about overtime, weekend work requirements and the specific duties. In some cases, you may need to provide written documentation of such things to personnel at your first job, to ensure that you are not creating a conflict of interest. If you can afford to, stick to a secondary part-time job or something you can do from home.
Evaluate the outside effects of your new schedule on both jobs. If you don't get enough sleep, this could make you late for one or both jobs and negatively impact your performance. It will also negatively impact your entire quality of life and could mean that you really won't be able to keep up with two full-time jobs even for a few weeks. You know yourself best, but be honest about how much you are capable of taking on.
If you are unsure of whether you can legally hold a second full-time (or even part-time) job while staying at your first job and not get fired, you should check with your boss to get a clear idea of the policy. Explain why you need to take on a second job and how the other job you are considering would in no way conflict with your duties. However, be aware that your boss might take this to mean you are looking elsewhere or are unhappy with your pay and position. Use your own judgment, and never compromise the job that pays better and offers more security or upside opportunity with a job that only offers additional cash.