Blue necklaces come into their own around now, when everything in the shops has gone black, grey and camel and your neck is crying out for a bit of colour that isn't Christmas red. A blue pendant against a plain jumper does more for a dull outfit than another pair of earrings ever will, and it works just as well in April as it does in December, which is more than I can say for most of my sparkly stuff.
If you've got none, start with a single small stone pendant on a fine chain rather than anything chunky or statement. It's the one that goes under a collar, over a roll neck, with a blazer, with nothing, and it won't fight with other jewellery while you're working out what you actually like. Chunkier blue pieces, beaded chokers, big glass drops, are brilliant but they want a plain outfit built around them, and I learned that the hard way wearing a lapis style bib necklace with a patterned shirt that already had enough going on, the whole thing looked like an argument.
On colour, go for a mid or deep blue before you go near anything pale or bright. Navy, sapphire, that proper denim blue, these read as almost neutral and sit next to gold or silver without a fuss. Pale blue and turquoise are gorgeous but they're pickier about what they're worn with, and a very bright cobalt can start to look like a costume piece rather than jewellery if the stone's too big. Mixed finish pieces, a blue stone set in a slightly aged gold setting rather than a shiny one, tend to look more expensive than they cost and age better too.
How it wears depends almost entirely on what the blue actually is. Genuine stone, like lapis or turquoise, is porous and will dull if you're spraying perfume directly onto it or swimming in it, so put it on last and take it off first. Glass and enamel blues are tougher day to day but enamel can chip at the edge if it knocks against something hard, so I don't wear mine gardening, not that I garden much, but you get the idea. Either way, a soft cloth after wearing and keeping it away from the bottom of a jewellery box full of chains it can get scratched by will keep it looking right for years rather than months.
In the shop, check the setting holds the stone properly with no visible gap or wobble, check the clasp actually opens and closes without three attempts, and hold the piece up to see if the blue looks different in daylight than it did under the shop lights, because it very often does.