Download the SlideME Application Manager (SAM): http://slideme.org/sam.apk using the browser on your Android device. From SAM, you can discover, view, download and purchase applications. (You may have an optimized version of SAM preloaded by your device vendor. Its suggested you keep this or contact support for a later version if one is available).
You have two options to purchase applications.
You can either create a Billing Agreement under "My Actions" drop down menu > "Billing & Payments" menu or use the WebBUY option and SlideME Wallet. For more information regarding the different payment methods and what is more suitable for you, see faq Which payment model best suits my needs?
Free applications can also be downloaded directly from the SlideME website. The download link is displayed on the application description page.
Most prefer using SAM for better user experience, since from one single application you have access to all applications available on the SlideME Marketplace.