I want to get the database of the images taken by Landsat satellite of Earth for a project. I searched and searched and searched, but
Head over to the USGS website, and find yourself their nifty Earth Explorer webapp. Figure out where & when you want to snag the imagery of (the tools they provide allow you to draw/designate an area of interest), and then select the data product. Since you're interested in Landsat, you'll navigate like so: Data Sets-->Landsat-->Landsat Collection 2 Level-2 (This is the most processed data & the easiest to view casually). Then choose which satellite(s) you'll want data from. Note that while Landsat 7 has a much longer history than Landsat 8, it's got a problem that makes its pictures a bit missed up. Nothing insurmountable if you don't mind doing some post-processing.
Then you'll get a list of scenes (single images, in multiple spectral bands) for the location(s) and times(s) you indicated. Download whichever you want--but be warned! Each full multispectral scene is BIG--around 100 GB a piece give or take, if I recall correctly.
Also you'll need to make a USGS account & give the folks over at the offices a reason you want the imagery. Moving that kind of bandwidth isn't cheap.
- Very recent data probably isn't available in the level 2 datsets because it's still being processed.
- Not every location is imaged at every time--the repeat time on Landsat orbits is 14 days.
- Don't be surprised if what you're trying to see is covered in clouds. There's a tool that filters out the most cloudy images.
- It's going to be downloaded as massive GEOTiffs, so be prepared to handle that file format. ArcGIS or qGIS will be your friends.
If for whatever reason you can't get approved, check out Google Earth Engine for a more complex but more modern approach to messing with geospatial imagery that doesn't involve downloading TBs of data to your personal hard drive. Google does that for you.