The v3 cart upgrade is a per-store upgrade. If you are new to DPD or have created a new store (as of February 10, 2015), you don't need to do anything. You already have the new responsive cart.
First Generation Vendors:
If you have have a link in your left-side navigation menu that says "Upgrade Cart!", then congratulations! You've been with DPD for years an have our our first generation cart from two versions back. Thank you so much for using DPD, but its time to get up with the times. Click that Upgrade Cart link and you'll automatically upgrade to the latest and greatest. You have no more to do.
Second Generation Vendors:
If you don't have that Upgrade Cart link, then you're probably on our second generation cart. The new cart generations are theme based, so you just have to create a new theme and apply it. To do this, look under the Look and Feel section of the left side navigation menu. Click Theme > Create New Theme. Enter and name for your theme and save.
From here, you have a new theme, but it isn't applied yet. At the top of the new theme, you'll see a Preview Theme button and a Use button. If ready for the new cart, just click Use, which will apply the theme.
New Theme Preview:
If you want to experience the new cart before you commit, you can click the Preview Theme button. This will open a new window with the new cart in it. Unlike the old Theme Preview, which mocks a dummy page which looks like your cart, the V3 Theme Preview loads your theme into just your browser session and sends you to your actual cart.
Once you're previewing your cart, you can go back to the theme page and edit things to your liking. When you click save on your theme assets, they will take affect on your cart session only. Its only when you click the Use button that the theme will be applied to everyone else.
Special Note for Late Adopters:
At some point in the near future, we will force the remaining first and second generation carts to our latest v3 responsive design. Traditionally, we at DPD have always supported previous versions of our cart, however, we made this decision in effort to reduce the burden of maintaining multiple versions and enable us to focus on making a better product for everyone.