Your fin is your rudder, the motor, and steering wheel. It all comes down to how your fin interacts with the water and the rail of your surfboard. Change the fin, change the ride.
We have all at some point on our surfing journey been faced with a wall of fins in a surf store or online. They all look beautiful, fun, and the same to start with .. which then leads you down the 'which one looks prettiest' path .. So we hope this quick overview can help in your surfing life, but do always get in touch for further advice. 
One of the most important choices in Fins will come down to how you want to surf your board, the board type and the predominant wave types you will be surfing. 
The most prescribed bit of help on this, is that for every foot in length of your board, look for an inch in height on your fin. This gives you an ok starting point, however, Tail Width is the most important design feature in relation to your single fin length. You should lay the proposed fin down on its side on the fin-box position. You are aiming for 1/3 of the fin length to be hanging over the rail of the board. If you are picking a fin online.. use a tape measure at home. This information came to us through watching CJ Nelson talk fins on his Flow(ish) Friday videos (screen shot below), and I believe he got this off Marc Andreini whom got it off the legend Rennie Yater. 
Once you've got the height of your fin, you've got the base length of the fin, and overall surface area to consider. A larger surface area will increase hold (control) and drive (generated speed) but could ultimately slow your board down 'in trim' because of the increased drag (great for nose-riding). A smaller fin will increase sensitivity and reduce drag, making your board go faster, but will reduce hold. That’s why it’s important to create a balance of these aspects to best compliment the wave conditions and style of surfing desired.
George Greenough illustrated above was the forefather of performance fins inspiring Nat Young and Bob McTavish to re-foil their traditonal pivots into raked back fins built for turns.
We keep going back to style, board type, and wave type, and that will effect the following aspects too.. Rake, Placement, and construction. 
This is majorly important in your surfing style. And once you have found your rake, using a fin with different rake on the same board will completely change it. A more upright fin (less rake) will provide your board with a tighter-arcing radius. Fins that are more swept back (more rake) will draw out your turns. If you are on faster, bigger waves, that raked fin will allow more control and more power in the turn, with bent knees and body torque. The upright fin will give a quicker, easier pivot turn using your ankles, with a more up right body, and a more 1960's longboard style. Of course people are blending these, and compromising for their exact needs, styles and surf. 
If you're having a board made, you can stipulate to the shaper where you want the fin box or glass on fin to be placed if you already have knowledge, and if foam thickness allows. Most of the time you will get a board, with a single fin box, and depending on the base length of your fin, you should have some wiggle room back and forward, to adjust the feel. Placing the fin forward creates a looser feeling. Putting the fin towards the rear of the box can stiffen up the board and provide control. We always recommend playing around with the location of your single fin until you have found the sweet spot. Some fins and boxes allow zero movement, because the shaper has already figured out exactly what you need to do and which fin to recommend. 
In weaker waves or for particular jivey surf styles, flex in the fin can help to perpetrate delayed drive and spring through turns. Flex will often be found in fins with more rake and less surface area. For powerful surfers or in surf of consequence, you're unlikely to want any surprises, so a thicker lay up of fin or a construction using G10 fibreglass will ensure the fin is solid through turns, and gets you to your destination on time.
Check in with our available fins here. We hope that helps.
All illustrations by Phil James.