I used to HATE soldering. Seriously. It gave me a headache, I always struggled to get the solder to flow, and I accidentally melted more pieces than I can count. So I'd avoid it like the plague, which is why I used to work almost exclusively with wax, even when the design would've been better suited to sheet metal.
I think a lot of beginner metalsmiths have similar problems, probably because most of us are partly or fully self-taught. Which is great, but that can sometimes mean that we've neglected some of the basics.
Before I go any further in this post, I'd like to give out a few disclaimers. First, this isn't a soldering tutorial. There are so many of those on Youtube! If you're completely new to soldering (like, you don't know how to do anything at all), I suggest checking those out. This post is more suited to metalsmiths who technically know HOW to solder, but maybe don't know how to do it well, or even easily.
Second, soldering is chemistry, and chemistry is the only subject I almost failed in high school. So whatever it is that's happening scientifically, I honestly couldn't tell you. I only know what I know from trial and error.
Third, because soldering is chemistry, and each metal has different properties, soldering each metal is a different process. At the moment, I only feel 100% confident in soldering sterling silver and 14k gold, since it's what I really do most often. I can't really give you advice on soldering brass, bronze, or even other karat gold.
Another thing. I'm not the end-all, be-all authority on soldering. I'm mostly self-taught. There's probably a better way to do everything I do, but this is just what I've personally found super effective. That doesn't mean other metalsmiths' methods are wrong.
Okay, here we go.
SAFETY FIRST
The reason I used to get such bad headaches when I soldered was that I stupidly pretty much ignored all safety precautions. Don't do this! You're literally igniting toxic fumes, which is horrible for your lungs. Make sure to use a respirator and have proper ventilation (here is some good advice on ventilation and fire proofing your soldering station). If you're soldering outside, make sure it's not somewhere where the wind (and therefore the fumes) will blow right back in your face.
TORCH
Many people are surprised to know that I don't use a propane torch. It's a great option for most jewelers, but honestly, having the stuff in my house scares me. I use this butane torch for everything and I swear it's never done me wrong.
SOLDERING SILVER
Personally, I use medium wire solder. If you're soldering various elements on a piece (ball accents, flowers, leaves, etc.), you will want to play around with different types of solder (extra-easy, easy, hard). However, I don't really make that kind of jewelry, so I'm probably not the best person to advise you on that.
I like this flux, which is what helps the solder flow, because it prevents the flux from burning off and reduces fire scale. Remember that it's toxic, so please use proper protection while soldering.
The most important thing to know is that the solder will flow toward the part of the metal that is the hottest. Say that I'm soldering a jump ring to a piece of sheet silver. In that case, I would focus the flame on the sheet, since the jump ring is smaller and will therefore heat up quicker. If the jump ring heats up faster, the solder will only stick to the jump ring, rather than to both the jump ring and the sheet.
(Note here how I focus the flame on the hamsa, rather than the smaller bail, until the metal turns pinkish-white, which means that the solder is ready to flow)
The same would be applicable if I were to solder a ring shank to the backplate of a bezel setting. Since the ring shank would almost certainly be smaller, it would heat up faster, meaning that the solder would only stick to the shank and not the backplate. Therefore, I'd focus the flame on the backplate.
If I am soldering two pieces that are roughly the same size, I'll simultaneously focus the flame on both.
(Note here how I alternate the flame between both rainbows, as they're both the same size. However, when I solder the jump ring onto the top rainbow, I focus the flame on the rainbow until the solder is ready to flow)
Soldering bezels to their backplates used to be the bane of my existence. Then I found this video, which saved my life (okay, maybe not my life, but it saved lots of bezels from melting). TRY IT. Life-changing, I'm telling you.
It's important to know WHEN the solder is ready to flow. With silver, it turns a white-pinkish color. Leave the flame on it too long, though, and it'll turn bright red and the silver will eventually melt.
REASONS SOLDER WON'T FLOW
If the solder just isn't flowing, don't keep the flame on the silver (or any metal, really) for too long. You'll just end up creating more fire scale and melting your piece. If the solder isn't flowing how it should, it could be due to a few of the following reasons:
Your silver is dirty. Stuff like dust, for example, will prevent the solder from flowing.
There's too much fire scale (i.e. when the silver turns blotchy and red). Dump it in the pickle for a while and try it again, once it's white and clean.
You've burnt off all the flux. Dump the piece in the pickle, clean it up, re-flux, and try again.
Your flame isn't strong enough. You might need to refill your tank, re-fuel your butane torch, or just turn the torch to a higher setting.
SOLDERING GOLD
I actually find soldering 14k gold a lot more straightforward than soldering silver. I use easy wire solder. Unlike with silver, where I focus my flame on the larger piece of metal, with 14k gold I actually just point my flame at the solder until it melts. Super easy.
The only thing I do differently is when I'm soldering a bezel to its backplate. In that case, I use the exact same method that I use with silver (i.e. that life-changing video I shared earlier!), and it works perfectly.
Don't be alarmed! When your gold solder is ready to flow, the gold will turn a bright red color. When soldering silver, that usually means that your silver is about to melt. Not so with gold! It just turns that scary color when your solder is about to flow.
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I hope all of this was helpful to you. Like I said, there's many different ways to do things, but this is just what works for me.