After you upload your pic to Photobucket, you'll see it below on the page. Under the photo, copy the "Direct Link" URL.
Then, come here and when you're ready to put in the picture, click the little icon above that looks like a little yellow square with mountains in it.
You'll get a little pop-up box. Enter the URL you copied in there, then click "Ok."
Voila! Your picture is in your post.
If the picture is too big, you can go back to Photobucket and click on the picture so that you have the detailed screen.
Above the picture, mouse over the picture itself and you'll see a menu along the top of the photo. Mouse over the "Edit image" link and click "Resize" from the drop-down menu.
On the following page, use the sliders to make the picture smaller. Click and hold the slider to move it, and they will both move to keep the dimension of the picture the same.
Once you have it the size you want, click the "Apply" button. Then just follow the same steps detailed above.