My big secret is to tin the wires first. After stripping the wires, apply some flux so the solder will stick easily and tin the wires. I like flux pens like these: https://www.amazon.com/Soldering-Electronics-Tabbing-Welding-Maintenance/dp/B0953NGKXR. TInning without flux is a big pain. And the pens are great for working on PC boards if you do that.
Once both side have been tinned, the two sides will stick quickly. And use heat shrink tubing.
Not quite related, but if you expect the wires to be flexed at all during use, I highly recommend silicone insulated wires. The insulation is flexible and usually the strands of the wire are very fine so the whole thing will be flexible. https://www.amazon.com/BNTECHGO-Silicone-Flexible-Stranded-Tinned/dp/B09X45RZCQ It's not super cheap, but after debugging two cases of thermistor wires broken inside a cable chain I decided to take the plunge and I'll never use the cheapo stranded stuff again.
Lastly, a good soldering iron is a good investment. I have one like this that I like: https://www.amazon.com/dp/B07Z3KCVCL
PS - and get a little tub of tip-tinner to refresh the tip of your soldering iron when it becomes hard to melt the solder on it. https://www.amazon.com/Thermaltronics-FBA_TMT-TC-2-Lead-Tinner-Container/dp/B00NS4J6BY