The more recent versions of Windows have an image resizing facility built into them but my own preference would be to use Irfanview, which is a free image viewing and editing program which deserves a place on everyone's computer. (it also works on all versions of Windows).
Download and install the program:
http://www.irfanview.com/
Then open your picture in Irfanview.
Go to Image > Resize/Resample
You'll see lots of complicated looking options but just choose a suitable size from the panel on the right. (640 x 480, or 800 x 600 will be fine for most purposes). Click 'OK'
Then go to File > Save As. Check that the file type is set to JPG (not to the default BMP), choose a suitable name (such as 'MyDogX' instead of the original 'MyDog'), ensure that the location is where you'd like it to go, and click 'Save'.
You can then close Irfanview and (using Outlook) create a new mail, adding 'MyDogX' as an attachment.
Chris