Things you will need to flask orchid seeds. You need Sealable Flasks, media, a sterile work environment, A way to sterilize your flasks and media, a place to incubate the flasks once sown, and a touch of knowledge.
Highly recommended equipment:
Optional Equipment that will make your life easier, but not necessary:
All of these things can be very intimating to someone just starting out, and expensive if you go top grade. Luckily, with a little knowledge and practice, most people can start flasking in their own home for only a couple hundred dollars, or even less if they already have some common kitchen tools.
Flasks: I reuse 24oz. glass pickle jars for my flasks. They have nice wide mouths so you can easily replate or remove plants without damage, have resealing lids (I wouldn't recommend using resealing for food stuff, but it's more than fine for orchids), and come filled with free pickles. just make sure to wash them good.
Media: I use Phytotech P668 media broth at half strength for Phals. The recommended recipe for Phals is 100ml water, 1.5g agar, 1.37g P668 media broth. I highly recommend just buying the media from PhytoTech, as there are many home made recipes, but most will cost you far more than the $12 for the 10L bottle in the long run, and will add many more potential failure points. With P668, you will need to buy Agar as well, Agar can be bought from PythoTech as well as most healthfood stores. I usually use 100ml per Flask, and at that rate you should be able to get about 100 flasks for that $12.
However the precise formula of the media depends on the orchids you are growing. For example I used P668 for Phals, But P723 (terrestrial mix) for Calopogons. usually a quick google search will tell you the mix most commonly used.
Mixing Media: Your Agar must be "bloomed" to properly gel. To do this you heat the water/agar to a boil, then allow it to cool. You can do this in a pot on the stove, Jar/Breaker in a microwave or Stiring hotplate. Be careful of boilover. it can make quite the mess. Once the Agar has dissolved, add the 'media broth' and allow to dissolve. The media should be around 5 PH, and can be adjusted with vinegar or Baking soda as required. Pour into the flasks and allow to cool to ensure proper gelling. Place flasks in pressure cooker (lids slightly loose, to avoid the jars from exploding) and heat for at least 20 minutes at about 15 psi. I usually let it run for about 1hr once it is up to pressure, but this is to make sure the insides of the flasks fully heat up. A real autoclave would be better, but for home flasking, I can't justify the cost
Seed sterilization: The surface of your seeds will also need to be sterilized, but care must be made not to damage the embryos when sterilizing. For this a .5% solution of sodium hypochlorite is created. Be careful, this part can get tricky. Household bleach was commonly sold as 5.25% sodium hypochlorite, making the initial common sterilizing formula 10:1 Water:Bleach. Problem is now, there are other % of sodium hypochlorite in bleaches and bleach concentrates. Make sure you are checking the concentrations in your bleach (some are as high as 10%) so you'll need to adjust the amount of water to get the final amount of .5%.
This is where the syringe comes in handy. soak the seeds in the bleach mix for 10 minutes, then using a coffee filter over the end of the syringe, allowing the water out, but keeping the seeds in, squeeze out as much of the bleach solution as possible. Draw in as much sterilized clean water, Squeeze that out as well to rinse, and repeat at least 3 more times.
Sterile working environment: A laminar flow hood is a nice piece of equipment to create an easy to work in space, but they aren't cheap. Alternatives include a sealed Glove Box or Steam Column workspaces. Each has their pro's and con's, but they both have the benefit of being cheap and easy to set up. If you need links for either of these, I'll send them later.
Incubator: This really can be any place out of direct sun, but with at least 1000fc light and a temp of about 28'c, at least for Phals. You can construct a decent incubator out of some high intesity LED lights and a reptile heat bulb. But I know a one person that simply puts his flasks in a desk draw with LED lighting. This doesn't need to be fancy, just warm and bright.
Lastly, Patience. You will need lots of patience, and be prepared for failure. I've lost many flasks to contamination even with decent equipment. It happens. but keep trying and you'll get it to work.