Newbie GIS user here. Basic question about getting my raster (DEM) to align with my basemap. I've read similar threads but none of them make sense to me. In short, I have added a bing aerial layer in QGIS 2.10.1 and want to overlay four raster files. I can't get them to align properly, with the DEMs currently floating off the coast of West Africa. I've assigned the CRS for the project as WGS 84 / Pseudo Mercator, but can someone give me a guide on reprojecting the raster data to match the basemap.
Layers in QGIS may have different projections and if they are correctly assigned, the layers will automatically align because QGIS reprojects all layers on the fly to match the "Project CRS" (the Projection shown on the lower left (in your case EPSG:3857)
When you add a layer to the map and a dialog appears to choose a coordinate system means that no CRS system is assigned or the data is not georeferenced at all.
To see the assigned layer projection you can right click on the layer -> Layer properties -> General.
"currently floating off the coast of West Africa" means that they are located close to the maps origin (0, 0). That usually happens when the layer has no georeferencing because then the pixels are taken as the coordinates and they will always start at the origin OR the correct CRS has small numbers compared to the assigned CRS. That could be WGS84 (EPSG:4326).
Try assigning EPSG:4326 and see if the data matches. If not, compare Layer properties -> Metadata -> Layer Extent and Dimensions to verify.