Solid on Solid
A solid tie on a solid shirt is the easiest to match, you just have to understand a bit about colour. The best options are to choose a tie that complements the colour of the shirt, or one that is in the same colour family (analogous colours) as the shirt. Let me explain.
Complementary colours are ones that are opposite each other on the colour wheel, i.e Red/Blue, Violet/Yellow, Green/Pink-Mauve.
Analogous Colours and Shades
Analogous colours are the ones that are side by side on the colour wheel, i.e, a blue shirt with a dark green tie, or a violet shirt with a dark blue tie. You can also pair a light colour shirt with a darker version of that colour (light blue shirt with navy tie); using these combinations isn’t as eye-catching as complementary colours, but can provide a more subtly sophisticated look..
Solid on Pattern
Using the same theory as above, select the colour of the tie based on the one of the colours of the shirt. So, on a white shirt with a blue check, match your tie to the blue. If the shirt has two colours (like light pink with a blue stripe), pick the more subtle one; the tie will bring out the colour more. Complementary colours will stand out the most, but analogous colours can often work better.
Pattern on Solid
Patterned ties on solid shirts are also pretty easy; just match a colour in the tie to one in the shirt, the same as you did above.
Pattern on Pattern
The rules of pattern on pattern matching are a bit more complicated;
First – vary the patterns; avoid check ties with check shirts, etc.
Second – have the size of the patterns contrast – narrow striped shirt with a wide check tie, large check shirt with closely spaced dots, etc.
Third – match a colour in the tie with the primary colour of the shirt – if a blue check shirt looks blue, have part of the tie be a shade of blue.
The major thing to remember is to not go over board with the patterns; you should be able to tell the difference between you shirt and your tie from a distance, and people shouldn’t be getting a headache trying to figure out where one ends, and the other begins. When in doubt, remember KISS – Keep it simple, stupid.