NASA and the USGS both distribute full ASTER Level 1T scenes for immediate download and allow you to place orders for ASTER products. Examples of ASTER products include Surface Reflectance, Temperature, and Elevation. The full list of ASTER products are described at: https://lpdaac.usgs.gov/dataset_discovery/aster/aster_products_table.
If you are only interested in full L1T ASTER scenes, the USGS Earth Explorer site is very easy to navigate. Go to the Earth Explorer site, select the Data Set tab, then NASA LPDAAC Collections | ASTER Collections | ASTER Level 1T. Next select the location and time range you are interested in. You can also select the ASTER Global DEM product here.
We have several FAQs to help you search and download these data. Please read these separate ASTER FAQs: