It's pretty natural to want to work and earn some money while you're studying. However, since your stated purpose for being in the US is to study, you only have a few employment options available to you. Here is a very brief overview - more details on each can be found elsewhere (follow the links).
Option 1:
On-campus employment
You may work at any available on-campus position for up to 20 hours a week while school is in session (up to 40 during breaks). You must first apply and be hired for the position; get a letter from your DSO to take to your local Social Security Administration; get a letter of employment from your direct supervisor, which you also need to take to the SSA; and finally obtain a social security number. If your income qualifies you, you will be expected to pay US taxes and Social Security on whatever earnings you make. More detailed information for on-campus employment can be found here, and information on obtaining a SSN (which you need for any type of employment) can be found here.
Option 2:
Pre-completion OPT
Optional Practical Training allows you to work off-campus for up to 12 months total for each level of education you receive (bachelor's, master's, etc.). The job must be related to your field of study, and you are not eligible for OPT until you have completed at least one academic year. Pre-completion OPT can be either part-time or full-time, and must be finished before your program end date (graduation).
Option 3:
Post-completion OPT
Post-completion OPT must be full-time, and must take place after your program end date. Any time you have spent in pre-completion OPT will be subtracted from the full 12 months allowed you, and any remaining time can be spent in post-completion OPT. Much more detailed information on both types of OPT can be found here.
Option 4:
Off-campus employment
The only people who qualify for general off-campus employment are those who are undergoing an unexpected economic hardship that qualifies under the Department of Homeland Security's standards. You qualify for this type of employment only after you have completed one year of study. Talk to your DSO if you think you are eligible for this type of employment. More information can be found here.
Maintaining status means that you are fulfilling the purpose for which you were issued your visa (studying), and that you are following the regulations associated with that purpose. A student who fails to maintain status during his stay will be terminated in SEVIS and asked to leave the country at the least. Here are the regulations for maintaining status as an F-1 student:
Normal stuff
Going on vacation
Other things to bring up with your DSOs
Talk to us first if you need to do any of the following:
More details on maintaining your status can be found on the SEVIS site here.
Once your program completion date (or graduation date) passes, an F-1 student has 60 days to leave the country. There are a few ways to extend your stay in the US:
All international students have to file some form of documentation for taxes every year, whether or not they made any money. If you had no sources of US income during the last calendar year, you are exempt from taxes, but you still have to file an exemption form (bureaucracy at its finest). If you did make money from US sources in the last calendar year, you are required to file the appropriate tax forms, which may result in you having to pay taxes (although you might also get a refund). This guide walks you through how to determine what forms you need to fill out, what information you need, how to file, and what assistance is available to you.
If you are interested in staying in the US on a more permanent basis once you are done with your studies, there are basically two main options available to you: obtaining a temporary work visa, which grants you at least 3-6 years, or obtaining a green card, which grants you permanent resident status.
Work Visa
The H-1B visa, which is what a recent graduate would most likely qualify more, must be sponsored and applied for by your employer. You still have to compete with any other applicants for a position, but if you are the best qualified for the job, the employer can hire you. The US Customs and Immigration folks only grant 65,000 H-1B visas a year, and they are selected for approval through a random lottery process. You can find more information on work visas here.
Green Card
There are two ways for you to obtain a green card. One is to get married to a US citizen; after you have received a green card in this way, you will be eligible for US citizenship after 3 years. The other is to have your employer sponsor a green card for you if you have a permanent work opportunity in the US. This makes you eligible for citizenship after 5 years; however, you must be the only qualified applicant for the position, and if a US citizen applies who is only minimally qualified, your application won't be approved. Much more detailed information can be found here.