Let's get a couple of things out of the way:
What kind of solder are you using? It should be rosen core and not acid core.
Is it lead free? or Lead based 63/37 or 60/40?
Are you soldering surface mount or components with leads?
Next, when you tin the tip, wipe it off first with a moist sponge sponge or rag. You should have a nice shiny surface.
Typically the tip material should be iron clad.
What wattage of an iron are you using? Is it temperature controlled?
Sorry, for all of the questions.
Now, the MOST IMPORTANT PART. Don't drip the solder on the joints.
Assemble the kit with the lowest height components first. You generally can basically put all of the 1/4 watt resistors in the board first, but wire jumpers have a lower height.
Now take your iron and push the lead up against the hole. Try to apply solder to the opposite side of the iron, e.g. the pad/lead mechanical connection that you made.
Experience comes into play when trying to figure out how long to heat the components, A touch of the solder to the mehanical connection every once and a while until it''s hot enough to flow. Then flow the joint.
Don't disturb it until it's cool.
Some caveats: Lead based 60/40 solder was great for components with leads. It melts at a different temperature than it solidifies at.
Lead based 63/37 melts at solidifies at the SAME temperature. So, you take the heat away and instant solidification. It's essential for hand soldering of surface mount components without using pastes and a solder mask.
The EU created an initiative of ROHS or Reductions in Hazardous Substances. One of those substances is lead. The substitutions have reliability issues which are slowing being worked out, but soldering requires hotter temperatures and is more difficult.
You also need to clean the flux off the board. Isopropyl alcohol or Acetone on a cotton swap usually works. Do this early in the process. e.g. Don't let it sit a week.
I don't really want to comment on the respirator use. Fume extractors do exist.
Here
https://www.circuitspecialists.com/soldering-articles is some stuff that you might want to look at.