Ready Made LED Arrays
There are several places that produce and sell LED arrays, and these arrays may or may not provide sufficient light for the purpose. Those 11 LED arrays you can buy at your auto supply store are notorious for being way too dim. If you really want light, enough to replace an 1157 bulb, you need many more LEDs than that!
Custom Dynamics sells LED arrays that I have found to be quite bright. I used the 1.8 inch array in my taillight and found it very usable. My riding buddies think it shows up very nicely. This unit has 48 high output red LEDs, which are also called Super Bright LEDs.
Super Bright LEDs (the company)also has a good array of products. Some of these work well, others don't work so well.
Web Bike World has quite a bit of information on LED lighting, including reviews of many of the arrays at Custom Dynamics and Super Bright LEDs. I recommend spending some time at this site before buying a commercially made array.
Brightness
No matter if you are making your own array or buying one, it's a good idea to find out how bright the array will be. This can be difficult because companies either don't provide any specifications at all, or provide them in different units. To make matters more complicated, some measures are used over a spherical surface, while others are used over part of a sphere. In particular, LEDs emit light over a limited angle while an 1157 bulb emits light over a nearly a full sphere and often has a reflector to use the luminance emitted towards the back. This makes mathematical conversions between units used for LEDs and bulbs difficult.
LEDs do emit over a restricted viewing angle, compared to light bulbs. Most LED array producers choose a 30 degree viewing angle as a minimum. This relativity wide (for a LED) viewing angle might make the LED dimmer, but you can always put more LEDs in the array to make up for this effect. Wide viewing angles are good in traffic, right?
Based on my eyeball, the reviews in Web Bike World, and some conversion programs I found on the web, I think that a LED array with 90,000 milli-candela (mcd) and a 30 degree viewing angle is about what I want for brightness. This should (and did) provide approximately the same brightnesses as an 1157 bulb on the bright filament and with a reflector.
FYI, a tid bit I picked up somewhere, I don't recall where now, is that brake and turn signal lights need to be at least five times brighter than running lights.
Caution
Most LED arrays are not DOT approved. That's why they are not recommended for the road. Many people use them on the road anyway. It's your choice, and if comes to it, your ticket.

Designing an Array
I looked around and found some Super Bright LEDs at (of course) Super Bright LEDs The link leads to a data sheet for the RL5-Y5030, a yellow LED of 5,000 mcd at 20 mA and 30 degree visibility angle. Why yellow? I was building a turn signal!
If I want 90,000 mcd, that means I need 90,000 / 5,000 = 18 LEDs, right? Well, not so fast. The actual brightness of the LED depends on current flow, and that eventually, depends on the voltage the bike supplies to the LED array. This voltage varies somewhat with age, corrosion in the wiring, distance from the battery, current draw, and whatever the charging system is doing at the moment. So I wanted some margin in the design. For this reason, I choose a 21 LED array and decided to design it for a slightly higher voltage than I thought it would get, which will cause a slightly lower current, slightly less brightness from each LED, and perhaps, a much longer life.
The data sheet for my LEDs

says that each LED will require 20 milliamps forward current at a typical forward voltage of 2.4 volts to provide 5,000 mcd. Now, how do I get this into a circuit? The Series/Parallel Array Wizard comes to the rescue!

I chose 13.5 volts as that was a bit high for that area of the bike, and gives me a bit of margin on current flow and LED life. This also means that I don't have to worry about creating a regulator for the LEDs. From the data sheet, I picked a 20 mA forward current and a 2.4 Volt typical forward voltage. I used 21 LEDs, of course.
Building the Array
There are many ways to build a LED array. The first requirement is to physically mount the LEDs and the second, is to make the proper electrical contacts. I chose to drill 5 mm holes in a peice of styrene plastic my wife had left over from model railroad buliding. You can see the LEDs sticking out of the plastic, which I later covered with mylar, in this photo.

The mylar is for better reflections, though LEDs don't emit much that far off-axis.
The wiring was done in the time honored "breadboard tradition", where leads are bent and soldered to other leads. All of this is left up-in-the-air, without a circuit board, because this is a "one off" circuit and I could not be bothered to build a circuit board for two turn signals!
I don't have a picture of the turn signal bread board hookup, but I do have a picture of a similar job done for my licence plate lights. Here is the outside:

And here is the inside, showing the wiring:

While the wires are stiff, they will not be left hanging out in the air like that. I will cover them with clear packing tape in the tail light housing. For the turn signals, I used RTV as a potting compound and a strain relief, like this:

I don't think those wires are going anywhere soon!
Another well accepted way to prototype a LED array is to use Pref Board to build your circuit.

Pref board is available at most any Electronics parts house, and allows you to solder the LEDs from the back and make the circuit at your leasure. Why didn't I use pref board? It would not allow me to pack the LEDs in as tight and my room was limited.
Soldering and Wire Forming
LEDs, and most semiconductors, don't like their leads bent at the case. It is good practice to make the bends a small distance away. This will avoid possible case damage. I use a pair of fine needle nose pliers to do this work. I admit, I don't always do this, but it is good practice.
LEDs also can't stand too much heat on their leads for too long. I use an 18 watt iron with a silver tip. This is a tool I used when I did circuit board repair and has done well for me over the years. It's a bit small to work with typical motorcycle wiring, but just right for semiconductors.

A 40 watt iron, or even worse, a soldering gun, will likely destroy the LEDs before you even get a chance to power the circuit up.
The Result
'Nuff said:

Special Considerations for Turn Signals
If you choose to create, or use, LED turn signals, you also need to change out your blinker unit. The stock unit, like all blinker relays more than 10 years old, will only blink if it has sufficient current. This normally means 2 1157 bulbs per side. Now days, there are quite a variety of low cost electronic flashers that do not depend on current level. I found three types in blister packs at my local Shuck's auto parts store just by asking the parts guy if he had any blinker modules for LED turn signals.
Since my new, two prong, blinker unit cost me all of $5.00, I don't see any reason to buy the $15.00 load units you can get from some of the LED sites. Even worse are the $100 blinker units these sites sell for LED turn signals. If you like the patterns they produce, that's good. They can be entertaining if you have the $$. But don't think they are the only solution to making your turn signals blink!
Some people are thinking that LED lights will save on the bike's power budget, or at least free up power for other accessories. They do, for the most part. But LED turn signals don't. Think about it. How long are turn signals really on during a ride? And even when you are using them, they are blinking, that is, they are off half the time. While there are a lot of good reasons to go LED for turn signals, I don't think you will see any significant power savings.
The End
Its been fun. Hope you like this!