Reading a Smith chart
A Smith chart maps every possible impedance onto a circle. The centre is a perfect match to your line, the left edge a short circuit and the right edge an open circuit. The upper half is inductive and the lower half capacitive. Moving along a feedline rotates the point around the centre, clockwise towards the transmitter, at a constant distance that is set by the SWR. That's why the SWR is the same all along a lossless line, but the impedance isn't.
Stub matching
A single stub is a piece of open or short-circuited line connected in parallel with the feedline. Somewhere along the line, the load's admittance has a real part that exactly matches the line, and the stub cancels the reactive part left over. There are two such points every half wavelength. The calculation follows the standard method in Pozar's Microwave Engineering, and the lengths include the velocity factor you enter. Stubs suit VHF and UHF, where the lengths are practical, and single-band HF antennas.
Hairpin and gamma matches
The driven element of a Yagi usually has a feedpoint resistance of 12 to 30 Ω. A hairpin match shortens the element so it's slightly capacitive, then puts an inductor, often a U of rod or wire, across the feedpoint. Together they form an L-network that brings the impedance up to 50 Ω. A gamma match feeds an unbroken element at a point along it, using a rod parallel to the element and a series capacitor. Gamma matches depend on the exact geometry, so the values here are starting points to adjust with an analyser.
For matching networks made from discrete parts, see the L-network calculator, and for quarter-wave transformers, the coax stub calculator.
Questions
What does the centre of a Smith chart mean?
A perfect match: the load equals the line impedance, the reflection coefficient is zero and the SWR is 1:1.
Which is better, an open or a shorted stub?
Shorted stubs are usually preferred because they're less affected by stray capacitance at the open end and are easy to build.
How do I measure the load impedance?
With an antenna analyser or NanoVNA at the feedpoint, or at the end of a known length of line, which you then account for.
Why is my Yagi's feedpoint resistance so low?
Close-spaced parasitic elements couple strongly to the driven element and lower its resistance, often to 15 to 25 Ω. That's why Yagis need a match.