Okay, this is by no means, a hard and fast blinkie tutorial,
it's just a series of techniques I use to make blinkies.
I make them using flashing dots, or gradients.

Utena Blinkie using gradients

Various dots of light blinkies, the bottom one is an icon.

You will need PSP, Animation Shop 3, or comparable programs for this tutorial.
for the gradient one, you can use my set of blinkie gradients which you can download here.
This tutorial assumes you know how to use Paint Shop Pro and Animation Shop. I will work on one later with more screenshots. However it is really simple.
For a standard blinkie, start by opening a new image 150 pixels wide and 20 pixels tall.

Set your paint brush to 1 and with a light gray color add dots every 3 pixel, then use a darker grey and add dots next to them.

Then add a new layer, and add dots in the same colors just one pixel off the previous layer, then a third layer and add them one pixel off the second layer.
Okay! Save the resulting image as a psp file in layers to use to make new blinkies later. Go to windows/duplicate, (always best to work in duplicates!) Add a new raster layer(layer 4), then drag it to the bottom, color it whatever color you want it to be in the finished blinkie. This is your background.
Add any tiny images you want, and your text,use a font that can be read at around 8-10 points..It's easier to put them on new layers so you can get them positioned just right. Then click the glasses next to each of the top 3 layers where your blinkie part is to make them invisible and merge whatever layers you are working on for your base. Go to layers/duplicate, and duplicate that layer twice.
Click on the glasses next to the blinkie layers to make them visible again, then go to colors/colorise and find a shade that looks good to you. Do that on all 3 blinkie layers.
For a quick reference,
Hue 15-30 is a yellowish/brown color, 81-100 is a green, 130-175 is blue, 195-220 are purples and pinks, and 250-255, and 0-10 are reds.
Saturation chooses the intensity of the hue.

Now to start merging layers, turn off the visibility on the top 2 blinkie layers, and the top 2 background layers, click on the bottom layer (the first background layer) and click merge visible. Turn visibility off on that, then turn it on the second background layer and second blinkie layer, merge visible, then turn visibility off on that layer, turn it on the last background and last blinkie layer, and merge visible (3 layers now total).
Turn back on visibility for all the 3 layers, and save as a psp file. Now open up animation shop, and open that image. It should show it in 3 frames, hit the play button and decide if you like the blinkie effect at your default speed, if not, change the speed until you get it how you want it. Save as gif.

For the gradient one, unzip my gradients to your gradient folder, and open a new image 150x25 pixels, and fill the first layer with gradient fill, set to linear, 0 repeats,90 degrees., blinkie1, layer/new layer, blinkie2, layer/new layer blinkie 3, layer/new layer blinkie 4, save the image for another base template, windows, duplicate, close the original image.Then add a new layer, with your images and text, duplicate that layer 4 times, go to the gradient layers and colorise them using colors/colorise, then merge the gradient layers with the image text layers like you did before. Making sure you keep the gradient layers in the same order.
Save it with all layers visible, and open it in Animation Shop. Set it to the speed you want, and save it.

Blinkie with a side image

Open up one of your base templates. I chose the regular blinkie. Windows/duplicate, then closed the original image, then I went to image/canvas size, and proceed like I was making a blinkie as above, up to the point where I would I normally duplicate my text/image/background layer, making sure that instead of having things centered, I left room for the image I was going to put on the side. Then image/canvas size 200x200 pixels,I went to the top blinkie layer and layer/new layer, and I put the image in on the side. then I duplicated both the background layers, and the image layers twice, then go through the whole process of merging the 3 different types of layers so I had 3 layers again all over. Click in the transparent space with the magic wand tool, then selections/invert/crop to selection. Make sure all 3 layers are visible, save it as a psp file, open it in Animation shop, and animate!

This is by no means a hard and fast tutorial, and there are some out there that have many more screenshots and more information. This is just an overview of how I make them.
 

You can see my blinkies page here or go to my home page here.