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I am always a big advocate of honesty on an application. That said, there is such a thing as providing too much information.
In terms of providing a reason for leaving, you could say something like, "Personal situation prevented me from staying with company. Situation has since been resolved". OR "no longer a good fit for me". This might be a little bit of a stretch, but if you were fired because you were arrested, then technically it is still true!
One thing to keep in mind about applying for new jobs, is that the person reading the application is interested in somehow assessing whether you will not only be able to do the job, but also be able to do it well (no complaining, drama, or being unreliable).
That's a really hard thing to try to assess from a few pieces of paper.
One of the BEST THINGS YOU CAN DO is include a cover letter. Even if it is just a short paragraph included in the application (there is usually a text box for you to provide additional information). Because a lot of people don't provided a cover letter for entry-level positions, this helps your application stand out amongst the rest. It also gives you the opportunity to tell the reader why you would be a good employee.
One last piece of (admittedly unsolicited, sorry) advice. I'm assuming that because this was your first job, you may be applying for entry-level positions. This is in your favor, as hiring managers typically expect a shorter work history. That said, if you were only at your first job for a couple of months, it may be to your advantage to not include it at all. I frequently advise people who are new to the workforce to use things like volunteer activities, or advanced classes/class projects as part of their work history.