In today's world, anything is permissible for a monogram or set of initials - from cute and bouncy to illegibly floral to stark and severe - but we haven't been so culturally open in the past. Etiquette books are filled with guidelines on how to mark your linens - the colors, the initials chosen, even the placement!
For guys: No bright sunny colors here. Black, grey, and navy are perennial favorites, but plum, burgundy, forest green, and rich brown were all just fine as well. No oranges, pinks, or bright blues though. In a surprising turn, white is also a-okay. Multiple tones fairly common, but usually no more than two or three and in complementary jewel tones.
For girls: Black, grey, and navy were considered acceptable, if severe. White is always a favorite, especially to showcase a girl's embroidery talents. Pastel tones (and most especially blues) considered quite appropriate. Multiple tones common, especially with more decorated alphabets. Floral garlands and ribbons very common.
Should Alfred Bernard Constable lay out his initials ABC, or ACB? Either way he likes, really. If the larger letter is noticeably larger, ACB. If they're all the same, ABC. He can even do just AC, if he doesn't care for the Bernard:
If he goes with just one initial, traditionally, it's his last. Family honor, you know.
For girls, things are just the same - until you come to one single initial. What is poor Abigail Brown to do? She has to embroider her trousseau to be a respectable wife, but as soon as she marries, her last name will change. She's certainly not going to re-embroider everything she's spent her single life preparing. The solution: she uses her first initial! Though she might go from Brown to Constable, she'll still always be Abigail.
For guys, either the border is the plain hem, ornamented with the same color (like the cotton handkerchiefs with the woven lines by the edges) or with a single color edge. Lace, tatting, and other heavily decorated edges have been out for a long time.
For girls, the rules were a bit more relaxed. Handkerchiefs were a great way to show off cool trims, laces, and techniques, and hankies that have more border than usable hankie were not uncommon, especially at weddings. Lace, bright colors, even solidly embroidered scalloped edges are quite common.
For guys and girls, having the design centered in one corner is a common and useful place to put it. It doesn't get in the way when you fold it, it looks pretty when presented, and it's easy to read. Though it's the most common orientation, it's not the only one. Sometimes the motif is flipped around so the corner is at the top:
Parallel to the hem is another fairly common choice. This looks a bit more modern, and is great for longer lines of text where 'cutting off' so much of the corner with a design isn't feasible.The most common places are the bottom right and the top left corner:
Other placements, like the center of a side or the center of the handkerchief, are seen but are much less common. The placement of a motif on a handkerchief or pocket square was up to personal preference.
One thing to remember, though; according to the books, the embroidery should never be seen if a pocket square is folded in the front pocket. It's a hidden surprise meant just for you unless you share it. It certainly shouldn't draw too much attention away from the real star - you!