There's lots of Photobucket Tutorial videos on youtube but they all seem to be for the old style of Photobucket, here's a quick rundown of the steps written for complete noobs.
www.photobucket.com is the most popular choice for uploading and sharing pictures, it's free and fairly simple. Go there and sign up for an account, I'd explain this step but you being on this forum shows you already know how to sign up somewhere.
Before uploading your pictures make sure they are resized to about 600 x 600 pixels at the most, any bigger and they will be too large for most forums and make it hard to read the thread that you're posting in.
Sign into your photobucket account and click on the green button at the top of the screen that says "Upload Now"
Then click on the green button that says "Select Photos and Videos", a box will pop up where you can select various pictures from your computer but you may have to find them. If you don't know where they are I can't help you, just quit now.
You can select one and then hold Ctrl to select another, do this as many times as you like but remain in one folder or you'll lose your previous selections.
Once you have selected the photos/videos that you want click the button (in that same box) that says "Open", it will disappear and you see a status bar and percentage telling you the progress of your upload. When it's done scroll down and you'll be presented with a page where you can add a title, description and tags to each photo. Do this if you want, it isn't necessary but does make your album a little easier to navigate later.
Once finished there scroll back up to the blue text that says "Save and continue to my album". You'll be back at your album and see a thumbnail of each picture you've uploaded. Mouse over the picture you'd like to post and a box will appear below the photo. Click on the text that starts with http:// and it will automatically be copied to your clipboard.
The return to the forum and right click in the post where you'd like the photo to go and select "Paste", this will paste the code you just copied and when you click on "Preview Post" you should see your post with the photo instead of the code. Again make sure the picture is not too big or people will complain and it might get deleted.
Repeat as necessary....