I peeper and welcome to Orchid Board.
I usually give them a gentle tug, perhaps a slight tug and twist, and if they come away then that's that, otherwise I leave them and try again the next day. Eventually the plant will let go of them.
Buds can often drop after a change in enviroment. However it can be a good idea to check the roots on newly aquired orchids especially if some buds are dropping.
Is it in a clear pot? can you see some of the roots and medium?
If you can then do any roots look like they are dark and hollow? Healthy roots look bright green fading to a silvery green as they dry, (although sometimes the medium can stain them brown, firm looking is the key). If most of the roots look good then it's likely fine.
If you are unsure or can't see the roots it may be worth sliding it out the pot and taking a closer look. You can gently grip roots in your fingers (don't squeeze too hard, but enough to tell if they are firm). If they are firm (whatever the colour) they are good.
If you are new to orchids I will just give a bit of watering advice. Water with luke warm water and do so when all the roots (right to the bottom of the pot) are looking silvery rather than green. While they are green they don't need more water. It's best to water thoroughly with lots of water but fully drain after watering. Never leave it standing in water, even a little in the bottom, after watering. I stand it up to the top of the pot in water for 15min to water it, but then make sure it's fully drained. You can also run lots of water through the pot to water it.
If you don't have a clear pot to judge watering by root colour then you can use a wooden skewer in the pot. Leave it in , and pull it out when you want to see if it needs watering. If it's still damp it's not time yet.
I will just add for completeness that you will probably read about watering methods that don't dry it out in between. My suggestion is that for beginners the method of drying out between waterings is the easiest way to avoid root rot and unless you are in an extreamly dry enviroment should give the plant the water it needs.