Whenever you are soldering you should use some kind of ventilation, such as a smoke absorber. It could be a ceiling fan, an open window or a filter on your worktop. Tabletop ones are best for stopping the smoke at the source.
The tabletop ones go buy various names and I have seen them called smoke absorbers, smoke filters, soldering filter, smoke extractor and more. We like this model, Aoyue Benchtop Solder Smoke Absorber
Or you could make your own like the ones listed below.
Shark Fan by Instructable user AmatuerHour.
Using plywood and two scavenged computer fans, this build was inexpensive but creative and came out great. You could take this idea and build other animals instead of a shark.
If Sharks are not your thing, try making Solder Fume Extractor by ThomasVDD on Instructables. ThomasVDD uses a computer fan, filters and some Tupperware for the box.
Another good cheap option. Make sure you use heat shrink over the connections you solder to connect the fan to the wall wart plug. You might even want to put electrical tape over the heat shrink.
Solder Smoke Air Filter from CaptPikel on Instructables is in the same cheap vein as Solder Fume Extractor above, but uses a cardboard box instead of Tupperware.
CaptPikel uses velcro tabs to attach the filter to the front of the cardboard box and also cleverly bends a coat hanger to use as a stand.
And here is one from Oscar Liang using a cool orange 3D printed enclosure.
This smoke absorber uses a 3d printed case, batteries, voltage meter. We like that this uses batteries instead of soldering the fan to a wall wart type of plug as this could potentially be dangerous if not done correctly.
3/10/2020
New find, a led light and smoke absorber all in one! Adjustable LED lamp that clamps to your DIY work table along with removable charcoal filters and a fan.
3-in-1 Solder Smoke Absorber Fume Extractor Fan with Carbon Filter LED Lamp
Make your own or buy a smoke absorber, just remember to use ventilation when soldering!