Go to to twitter.com and sign in.
Click on settings in the top right menu and then click on picture in the menu.
Click on browse to choose the image from your pc that you want to upload to your twitter account.
Remember your picture must be 700k or less and it must be a JPG, GIF, or PNG.
Once you have chosen your picture, click save and your new picture should show up.
After Signing in to twitter go to your profile page(it will be like twitter.com/YourUserName), click on the edit profile button (given on the right side on your screen). After this you will see text saying "Change your profile photo" along with camera icon, click there. After this you will see 4 options. Upload photo will be the one of these, click on it and then select the photo you want to set as your profile picture.