How to learn a new hobby starts before you ever pick up a book, tool or put the required spandex outfit.
The How starts with research. Lots of it.
Try and get all of your research done before you buy anything, or even get started. Quite often in carrying out the research you will discover more things you needed to know, things you hadn’t thought of before you started.
When researching your new hobby, be open to similar things. Maybe you want to learn to fly a plane? Don’t forget to check out microlighting, powered paragliding, gliding etc. Microlighting is a cheaper route to the same pilots licence, or maybe it is actually what you want to be doing?
Try looking in a variety of places. Just as price comparison sites really only check a small proportion of companies, so if you search for “Running Shoes” in google, you will only find the tip of the iceberg.
Amazon, Ebay are a great way to start finding equipment, the former being great for equipment reviews, but quite often going into a shop and talking to people is what you actually want. Maybe you are wanting to learn to rock climb? Buying rock climbing shoes from amazon is fine, you can return them so can start to find the right size fit, but go into a shop and you can try on ten pairs, whilst being advised by an expert who can show you exactly how tight they need to be and how to test them.
Finally don’t shy away from courses. Teaching yourself archery is going to be very hit and miss. Without someone there to show you how to set up, hold the bow/arrow, draw and release, if you do ever get there it is going to take far far longer than a short course from your local archery course, that will invariably be cheap and fun. You’ll also have the chance to ask about equipment, work out what strength bow you need, what arrows go with this, maybe you can rent a set from them for a short time to get to grips with it?