Find an image uploading site - I use Imgur: http://imgur.com/
Click on 'upload images' at the very top of the page above. You can then search your computer for pictures and/or drag and drop files into the space (you'll see what I mean) and once you have chosen your pics to upload, simply click 'start upload' and there you go.....
Once uploaded, on the right, you will see various links so that you can share your pics - I use BBCode, and you can change the size if you want (just below) from original, to small or large thumbnail etc. If you've uploaded several pictures, they will be numbered just above the picture you've just uploaded - to get the links to share for each picture, just select pic 1,2,3 etc and new links for each pic will appear on the right......rinse/repeat the copy link procedure for each one you want to share on the forum.
To simply copy the link to share, if you click the little icon next to BBCode, it will auto-copy the link and then you can just right click and paste it into your forum reply box and that's it!!
Note, if you leave it set at original size, the forum will auto resize it for you, but there will be a yellow banner at the top of your pic so that those who want to see the bigger picture can do so.
Hope that helps!