Where to begin:
Hyperflash/Plug and play for signal lamps.
Theory: LED bulbs don't play nice because they have a low draw, and the electrical system doesn't see that a bulb is in play, thinks the bulb is out, and double flashes as per FMVSS/CMVSS guidelines for automobile safety.
There are three ways to solve this issue.
The first. Untested, but probable if you can get it done: The Ford BCM, legend has it, can be told to not hyperflash via some very easy programming that turns off the double flash for low draw bulbs. It's a setting that I think carries over from vehicles sold for upfit or retrofit of emergency equipment. I can't outright confirm that the Fiesta BCM has this software switch because I got lazy and time crunched. If I had the time, I'd have found some tech with an IDS/VCM suite to log into my car and see.
The second. You can buy ebay LED signal bulbs that are internally resisted. 50/50 that they will work. They heat up a LOT and could damage your housings. Plug and play, but really questionable outcomes.
The third. In-line resistors.
https://www.youtube.com/watch?v=YKvzwq___P4
Tutorial as above. Not a good tutorial, but you can google a few others to round out the knowledge.
Specific to the Fiesta, you'll need four load resistors to do this properly. One for each corner. Get a multimeter and probe the connectors with a good view of where the wires go. With hazard lamps on, you will get a 12v pulse in the active signal line. That is where one end of your load resistor will splice to. The other will go to a ground in the harness. On the Fiesta front lamp connectors, the ground you will need is the one that is all alone in it's row. No other wires will be beside it.
You will not need resistors for the wing mirrors. The four you install will balance the system out enough to cover the LED's you'l install there to complete the look.
Tutorial for that:
http://fiestamk7.com/viewtopic.php?t=643
Final note, please weather wrap or heat shrink your splices if you intend to get your car wet ever again. Copper will corrode and your harness will rot if you don't.
For all lights, here is a place to order it all in one go, and is one of the better one-stop shops for LED markers. They will also sell the resistors you will need if you don't manage to get your BCM to play nice via programming.
http://www.diodedynamics.com/store/led-bulbs-1/listed-by-vehicle/ford/fiesta.html
Brakes are dual intensity. Don't mess that up or your Fiesta will end up a few feet shorter in traffic one day.
For ALL bulbs, I recommend ones that are 360* output. That is to say, they throw light wide. The ones you see that only fire out the front of the bulb are useless and don't output enough useable light in the day.
For the headlamps and fogs I went with an LED headlamp conversion, noting that to do the headlamps properly, you may have to modify the housings depending on the kit you get, and that could affect water tightness over time. I'm not worried about that as new housings are cheap, but if you don't want to risk it on an experiment, make sure you get LED headlamps that can fit in the housing with no cutting.
You can find such kits on EBAY or locally via a performance lighting shop, but be sure to get ones that, again, don't have that massive nasty heat-pod on the back. If there are ones with flexible heat ribbons, those will be the ones to go for.
Above all, make sure the lights you install are useful in all lighting conditions. A safe Fiesta is a happy one.
If you need any more specific information about wiring or the like, just let me know and I will do my best to reply when I can.
it's an easy upfit, by the way. Took several hours of my time but the results are just lovely.