You can buy LED fixtures off the shelf, which are basically ready to go. I've seen these as puck-shaped lights that are basically designed for under-cabinet or shelf lights.
![enter image description here](https://i.stack.imgur.com/5b8We.jpg)
There are other pretty simple off-the-shelf solutions as well, such as using rope light.
If you are talking about using raw LEDs and literally doing everything yourself, it's pretty simple. You need to get some high output LEDs (pay attention to color temperature, beam angle, etc to make sure it is suitable). You can get LEDs in different packaging: clear/diffused, large/small, forward/side-emitting. Likely your best bet will be a large frosted one. How many you need will just depend on how much area you're covering, and how bright you want it.
![enter image description here](https://i.stack.imgur.com/GiGvM.jpg)
You'll need a DC power supply. The exact values are all dependent on what you use, so it's very hard to give an answer here. There are online LED array calculators available, which can give you something like this:
![enter image description here](https://i.stack.imgur.com/g8vMn.png)
One of the major disadvantages of serial wiring (shown here) is that if one LED is disconnected or burns out, they all go out. Finding which one is broken can be difficult, and if you've ever done this with x-mas lights you'll understand what I mean.
Another possible disadvantage of the DIY solution is that you are either going to have to come up with a nice way to package this all underneath, or you'll have a bunch of wires and bare LEDs hanging under your cabinets (maybe hidden by some moulding, but still). This may turn off future potential buyers. Off the top of my head, using some split-loom tubing may be a way to hide the wires and make it look at least half-decent.
![enter image description here](https://i.stack.imgur.com/fRC6V.jpg)
For a multi-bulb fixture the LED units do not want to be in the area where high heat is generated as would be the case with incandescent or especially with halogen bulbs.
CFLs have their own special considerations if they are used in situations with special types of lamp dimmers. Such special dimmers may not be compatible with LED lighting modules.
Another consideration comes in from the light quality and perception of what the lighted area looks like. LED lamps have a different light character than do other types of bulbs and mixing them together may be perceived as unpleasant in the extreme cases.
Best Answer
What have you tried so far? On those type of lights, I've seen two different ways to get the light out. First method is to twist the glass counter-clockwise by pressing on it and twisting. It will then pull straight out giving you access to the bulb. The other method I've seen is where there is a tab and you put a screwdriver in and the center cartridge pulls out.
Once you get at the bulb, remember to never touch a Halogen or Xenon bulb with your bare finger. The oils from your skin can weaken the glass of the bulb and shorten its life. Use gloves or a cloth to hold the bulb when removing it from the package and inserting into the fixture.
This video looks similar to your photo and shows how to open it using the screwdriver method.