Ok, here we go step-by-step :)
First thing you have to do is create an account with PhotoBucket or another site that offers the option to upload images (ImageShack, Flickr etc. do the same - choose one you like best).
In this case I'll use PhotoBucket as an example.
In PhotoBucket you create an account in just two steps:
Go to http://photobucket.com/ and on the top you find a sign up button:
When you click that you get this:
Fill it in and when you have created your account enter your username + password and if you're working on your own computer you can choose 'remember me', so you won't have to login again and again;)
Click 'sign me up' and if the name you wanted isn't already taken you get this screen next:
Click 'no thanks' to get a free account.
Then you get asked what settings you like for your default folder - I prefer to keep things private as you can see :)
And you're done :)
When you're logged in you have an option to choose which files (images you want to upload).
Just click the green button and a browser window opens and you can select the files you want to upload.
You can select multiple files at once - it only makes the upload take a while longer to get it's job done ;)
I'll chose one in this case.
Clicking on ok gives an option to browse to the file on your computer.
And voila you see your file appear :)
When uploaded you're guided to a page with options to add remarks etc.
I never use them, since I use my account for tutorials etc., but if you use it for pictures it might be handy.
Click 'go to album' at the right or click save if you've made changes and you're guided back to thumbnails of your images.
When you hover over the thumbnail there appear several options.
For How To Geek choose 'IMG code'. Rightclick on the link and choose 'copy'.
Go to your post in HTG and paste the code you just copied into the textbox.
And now your image should appear :)
Another option is to choose 'direct link' and just above the HTG textbox choose 'image', paste the direct link in there and click ok.
Edit: there are some options you might want to take a look at in Photobucket.
1) You might want to change your privacysettings. You find them when you go to 'home' > 'account settings'.
2) when you don't want to have to click go to album after each image you've uploaded you can skip this by clicking 'more options' right under the green upload button.
And then untick 'Add more tags and descriptions on upload' near the bottom of the popup.