Fine art printmaking has an established convention for how and where to sign, and what to use for your signature. It's done in pencil (not pen) close to the bottom edge of the print. The edition number is on the left, your signature on the right (plus the year, if you're adding one). If you're giving the print a title, this goes in the center, often in inverted commas. If the print bleeds off the edges of the paper, this is put on the back, or in the print somewhere.
A print is signed by the artist to indicate that it is approved, that it wasn't a trial print to check the plate, but the "real thing". A sharp pencil is used because this indents the fibers of the paper, making it difficult to erase or change.
Print editions are shown as a fraction, the bottom number being the total number of prints made and the top number being the individual number of that specific print. Once the size of an edition has been decided, it's not done to print any more as it undermines the value of the others. You don't have to print the entire edition at one time, you can do a few and the rest later, provided you don't exceed the total you set. (If you do decide to create a second edition from a block, the convention is to add the Roman number II to the title or edition number. But it's frowned upon as it lessens the value of your first edition.)
The prints in an edition should be identical. The same paper, same colors (and tones), same order of printing multiple colors, same wiping of the ink, and so on. If you change a color, for instance, that will be a separate edition.
It's also convention for the artist to make artist's proofs of the edition which they keep. Usually it's no more than 10 percent of whatever the edition is (so two if the print edition were 20). These aren't numbered, but marked "proof", "artist's proof", or "AP".
Trial prints (TP) or working prints (WP) made to see how a block will print, to correct and refine it, are worth keeping as they show the development of a print. Annotate the print with notes of your thoughts and decisions, and it makes for an interesting record. (If you get famous enough, gallery curators will be very excited to find these!)
It's convention to cancel (deface) the printing block once all the prints have been done so no more can be made. This can be done by cutting a prominent line or cross on the printing block, or drilling a hole in it. The artist then makes a couple of prints to create a record of the block having been destroyed, marked CP (cancellation proof).
Two other terms you may come across are BAT and HC. A print signed BAT (Bon à Tirer) is one which the printmaker has approved and is to be used by a master printer as the standard for printing an edition. The printer usually keeps it. HC or Hors de Commerce is a special edition of an existing print done for a special occasion, a commemorative edition.