"Fame will go by and, so long, I've had you, fame. If it goes by, I've always known it was fickle. So at least it's something I experienced, but that's not where I live."--Marilyn Monroe

Okay, you get some good news.  Now what?

a.
Payment.

Small presses and literary magazines most often pay in contributors' copies, reduced rates on additional copies, subscriptions, and automatic contest entry.  Some pay actual money, but it will be modest, probably in a range between $25 and $250.  A single placement of your work in a journal is not what's going to make you rich, but you'll have a nice dinner.

b.
Contract and Rights.

Read what you're signing.  Talk to somebody if you have any questions.  Normally, a standard contract prevails, in which you sign over limited rights.  There are occasionally other kinds of contracts, which ask for more than limited rights.

i. The norm is to sign over "First North American Serial Rights."  In this kind of contract you are agreeing to let the journal or press publish your work one time in the normal course of their publishing practice.  "Serial," here means periodical--that is, something not a book, such as an ongoing journal, magazine, or newspaper.  These rights assume, and by signing the contract you concur, that the press or journal is publishing this work as an original work appearing for the first time in the U.S. and Canada.  Upon publication, all rights normally revert back to you.  You still own the piece of writing, though it is often a good idea to check on this reversion.  The standard protocol is, if you republish this work, you give credit on an acknowledgments page to this journal or press as the place where the work originally appeared.  If you work with a press or journal that does not have any kind of extensive contract, this is the presumption of what you are giving over to them when you submit your work for publication.
ii. "Second Serial Rights," or "Reprint Rights," are what you are offering to a journal or press if you have already published the piece of writing.  Journals and magazines are not generally interested in publishing pieces that have already been in print.  This is more the province of anthologies.  However, some journals--especially when they are mounting special topic issues--are amenable to this arrangement.  Always be very clear that a piece of writing has been previously published.
iii. "All rights."  Yikes.  If you sign over all rights, or "full rights," you give up the right to control the use of this work again in any form.  The journal or press owns your work, and can republish or sell any other rights to the work without your permission and without any further payment to you.  Don't go here.  This is not normally any kind of service to the writer.
iv. Small riders, exclusions, or requests.  Often, especially with the advent of the Internet, presses and journals will ask for slightly expanded permissions--the right to reprint your work in an anthology done by the press as a ten year anniversary, for example, or the right to publish your piece or a section of it on their website.  These are generally to your advantage, and are in service to the writer as much as to the press.

  • ADVICE. Of course, you want to retain as many rights as you can, within reason.  First North American Serial Rights are a given, but the others are tolerably negotiable.  Something writers often don't understand is that they can cross out parts of contracts.  You don't have to agree to everything, even if that intimidating contract says so.  If doing so is rational, clearly cross out the offending language, and then initial the excision.  Most journals and presses will understand, though you may have to discuss this with them.  And of course keep copies of everything--contracts, permission agreements, editor names, addresses and phone numbers of presses, and so on.  You'll need them when your book is published.

c.
Editorial changes.

Sometimes editors will ask you to make changes in the manuscript.  Normally, you do not have to agree to these changes as a condition of publication.

  • ADVICE. Often these are style sheet changes for overall consistency, which help to standardize and make stylistically and grammatically coherent the entire contents of the journal.  The editors are not picking on you individually, but are looking to the best interests of the journal as a whole.  Style sheet changes, such as comma placements and the like, are innocuous enough, and normally you should agree to them without hesitation, especially if the journal is using a standard source such as the Chicago Manual of Style.  Remember that this is a one-time publication, and you can keep your own style choices in the piece itself as it goes out for further publication.  If the press is indeed using the Chicago Manual of Style, however, which is largely the national standard for literature journals, and they find very many errors, pay attention.
  • If you don't know what the Chicago Manual of Style is, or the MLA Style Manual and Guide to Scholarly Publication, or the Modern Languages Association Handbook for Writers of Research Paper, you should look into them immediately.  They are the keepers of the rules on punctuation and style.  Each field has its own style requirements, and these are the most common for writers.  The MLA style guidelines are often associated with colleges and universities, while the Chicago Manual of Style is more often associated with the publishing industry as a whole, though these are generalizations.  The research sources with journal information mentioned earlier will tell you if a press has a particular preference, though something submitted consistent with either style standard is normally acceptable.
  • If an editor asks you to modify your work for other reasons, listen carefully.  Issues of clarity are one thing, issues of censorship are another.  Use your own best judgment, and ask the opinion of others if you are in doubt.  It is flattering to get published, but be sure it is you who is getting published.
"When you publish a book, it's the world's book. The world edits it."--Philip Roth

d.
Short bio. 

The first thing you'll be asked for when your work is accepted is a short bio.  You may have been asked to send one along when you submitted to begin with.

  • ADVICE. Write one now, not later.  Writing several lines about yourself is a hundred times harder to do than it sounds.  Don't wait until the last minute--you will likely regret the person you will create.

e.
Author photo.

As with the short bio, though not as often, you will be asked for an author photo, usually black and white.

  • ADVICE. Again, do it now.  Black and white takes longer to process, and you have to shoot a whole roll.  After studying other people's author photos, choose a few poses you can live with, making sure that they are mostly head shots.  They'll get cropped to headshots anyway, even if you send something larger.  Then find a friend with a steady hand, a good eye, and a knack for recognizing perfect light, and use the whole roll on yourself.  But do it now--I'm not joking.  If you win a prize, they will want the photo even sooner.  Of course, it would also be a good idea to have a color photo as well.  Advances in technology are making publication in color much more common as it becomes affordable.

f. Galleys, galley proofs, page proofs, tear sheets.

These are all terms for essentially the same thing: a printed copy of your work the way it will appear when it is printed.  Not all but many small and most larger journals will send you these pages and ask you, as final proofreader, to look for errors of any kind.  This is important--if you miss something, then it's you who missed it.  No excuses.  Should you need to, this may also be an opportunity for some minor changes, though each journal's policy on this differs.  Check the instructions that come with the galleys.

  • ADVICE. Keep your changes to a minimum, and only if absolutely necessary.  If you have substantial changes you'd like to make, save them for the next publication of this piece, either in an anthology or a book.  Changes often cost money--certainly major changes do--and journals have to be strict about their change policy.  If they were to let you do this, then they would have to let everyone do it, which would sink the journal in no time.