For this guide I will refer to the colored geometric tiles as either colors, shapes, or by their geometric designations.
The "wildcard" tiles I will refer to as nodes since they are capable of taking more than one connection.
I will refer to connections as either paths or connections depending on whether I feel one has become monotnous sounding.
The shapes that mark the begging and end of a path that are emphasized with a color stoke along their outermost edges I will call terminals.

Many times it is not obvious where to start seaching out your path to solve a puzzle, but sometimes, there are certain indicators that can reduce the amount of calculation you have to perform.
Here are some quick examples:
The isolated corner shape:

Here you see there can only be one (or shoudl I say, "THERE CAN BE ONLY ONE!) possible way to connect the square terminal in the lower left corner. Whenever I spot this, I will make a connection to the nearest possible node and then look at the rest of the puzzle. Sometimes you will find that there can only be one possible complete path. This is rare but it happens:

Here I've determined that there is only one possible way to connect the red triangles so I have started my solution by creating this path.

Lacking any isolated terminals to begin with, I will then look for the shape and color with the fewest number of tiles. I will typically start by drawing a path with the fewest amount of connections possible and then start working the rest of the puzzle and making changes as I find what nodes need filling out.

When I find myself stumped on a puzzle I will take a closer look at the color path I am currently working on. Going throught shape by shape to see if I can rearrange the path at any point to fill any missing spots on nodes. If I can fill an entire node with one path's connections I will. Moving on from there I will determine if any of those nodes are necessary to complete any remaining paths. If so, I will re-route being careful to observe which angle I use to make a connection so that I am not blocking the path of another color.
When I run into a problem I will leave the paths that I have built in place as I ponder a solution. Doing this helps me to visualize possible corrections.
Try to memorize patterns. Some puzzles by necessity will offer small bits that are identical to a section of a problem you have solved earlier. Always look carefully at your solution before it fades into the next puzzle.

Some features are not immediately apparent when you begin playing this game. One of the most helpful things to know, is that you don't have to start a path over from the terminal you started at. Simply clicking on a node or a shape will delete any part of the path that falls afterwards allowing you to make a mid-course edit with minimal clicks.

You don't have to make every color connect to a wild card node. Sometimes you will find a three color puzzle where only one color ever weaves through the nodes.

You do not have to make a complete path with one color before trying another. You can stop anywhere you want and begin another color.

That's about all I can offer at the moment. I hope this helps you on your way to mastering this peaceful and relaxing game. :cheers: