If you already have another job and are interested in sideline work as a translator or interpreter, its possible, and many successful freelancers start out this way, waiting until the translation or interpreting work can pay the bills before quitting another job. In this situation, you have the advantage of taking as long as you need to build your business up to the point where it replaces your current income. However, you also have the challenge of staying productive and available to both your full-time employer and your translation clients. Translation, like all international business, is often a fast-paced industry, and clients who contact you may need a response to their inquiry immediately, whether they're contacting you about working for them, or about doing re-visions to a translation you've already completed. For this reason, if you'll be combining part-time translation work with a full-time job, it's important to choose your clients carefully so that you don't end up being unavailable when they need you. You maybe better off taking lower-paying work that doesn't have a tight deadline, rather than higher-paying work that requires you to communicate with the translation client during your work day at your full-time job.
If you either don't want or don't need to work full-time, starting a part-time freelance business as your only job is a possibility as well. Depending on your geographical location and language pairs, your main challenge may be limiting your workload to your desired schedule. In theory, the on-call nature of most freelance translation and interpreting work lends itself well to part-timework, since it seems like you should be able to simply accept or turn down projects as your schedule allows. In practice, this isn't always the case. When a regular client calls, its hard to say "No", since you want to help them out and keep them as a client; when no one calls, you cant do much about it. Still, many freelancers can and do make a go of it part-time. The main guideline to keep in mind is to organize and run your business just as professionally as you would if you were working full-time; your clients don't need to know that you work part-time unless they ask, so don't give them a reason to suspect that you're less committed than someone who works 40+ hours per week.
Part-timers of all flavors should pay special attention to business expenses as related to income. If you're interested in earning a healthy income even as a part-timer, keep in mind that all of your expenses are distributed over a smaller number of billable hours than they would be if you worked full-time. In this case, it's worth considering options that allow you to stay competitive and professional without spending top dollar; for instance trying a free or low-cost translation memory program, using a custom ring number instead of a dedicated business phone line, forgoing a laptop computer and cell phone unless you would use them for other reasons, and looking for second hand office furnishings.