There are flexible circuit available in the market, but also there are some DIY ways to make your circuit flexible. For wearable applications, this may be interesting.
Stretch PCB from STELLA project
flexible small Arduino from seeedstudio
DIY method 1: Vinyl Cut Copper Foil on Kapton Tape
Using a Silhouette Cameo Plotter to cut a flexible circuitboard from various materials. The circuit base material is Kapton, a material that can withstand the high heat of soldering. The conductive circuit traces are cut from a sheet of copper tape and transferred manually onto the Kapton base. Finally a soldermask is cut from very thin Kapton tape and stuck on top of the circuit to insulate everything that does not need to be exposed for soldering to.
DIY method 2: Etching Flexible PCB
You can design, print and etch your own PCBs from a flexible sheet of Kapton coated with a thin layer of copper. For this, you need a flexible PCB material. The etching process is same as normal PCB etching.
DIY method 3: Vinyl cut copper foil + fabric
Using a vinyl cutter to cut the traces of a circuit design out of copper foil with adhesive backing. The copper traces can then be transferred to a base to make a flexible circuit.
DIY method 4: Laser Cut Conductive Fabric circuit
You can cut fused conductive fabric with Laser cutter in the shapes of traces and fuse onto base fabric material to make fabric PCB. This works best with copper conductive fabric as you can solder components onto them later.
DIY method 5: Embroidered circuit
You can also embroider circuit connections with conductive thread. It can be simple stitch, but also use decorative stitch to play with the aesthetic of the circuit. As some conductive thread has quite high resistance for traces (wile copper wire has less than 1 ohm resistance/10cm, some conductive threads are few ohms/10cm) you have to take care that your connections remain adequate resistance for your use.