How can a Grade-11 Student avail TESS data and learn to process? As mentioned, I am a Grade-11 student. I have always been interested in Data Processing activities. This sums up my experience of working on Asteroid hunt Campaign under IASC (International Asteroid Search Campaign). I yielded more than 22 Preliminary discoveries at once. Now I wish, to hunt for KBO (Kuiper belt objects) and Exoplanets. Definitely, hunting exoplanets is not a kids' task, but I possess the ability to learn and process and render astronomical data under guidance! I am ready to do everything. I am more inclined towards searching Outer-Worlds than the inner objects! Mentor-ship in this regard will be gratefully appreciated. I have searched quite a few things but none helped. I'm a Zooniverse user too. And over there, project slots were filled by other Citizen-Scientists!
I'll use the TESS satellite as an example, which you might use to look at transiting exoplanets for example.


Go to https://heasarc.gsfc.nasa.gov/docs/tess/data-access.html this gives you a list of links to other useful TESS websites, data access and analysis tools. There are links here to get raw and processed light curves or even to get light curves for stars with known exoplanets. This page also explains what data are available.
What I want to do is look at some lightcurves. So you go to the MAST portal. First thing is to decide what target you want to find. There's a box at the top where you can type something in. Not every star in the sky will have data. There are limitations to the coverage and the types of stars for which data are acquired and you probably need to familiarise yourself with that if you are doing something systematic.
So I try HD 36705 (AB Dor, this is a star I know - about 6th magnitude in the constellation of Doradus. Up pops an image of the sky (on the right of the screen). HD 36705 is the bright star in the middle. In the centre panel you see a list of observations by whatever satellites are in the archive (not just TESS, but IUE, Kepler etc.) This star has lots of TESS observations listed. Each row is a dataset. You want the TESS lightcurves, which are some way down. You can identify them because they are labelled as "TESS", they have a little icon next to them which indicates you can view the data (see below), they are labelled with a target name of "149248196" and you want the ones which have an Observation-ID that ends in "-s".
These are lighcurves. You can quickly view them using the internal viewer, by clicking on the little lightcurve icon.
 The light curve viewer allows you have a basic look at the data, but you need to download it to do any analysis.
Click on the download icon  and put it on your own computer. This is a zip file. Unzip it. The good stuff is here:
inflating: MAST_2020-02-05T1007/TESS/tess2018292075959-s0004-0000000149248196-0124-s/tess2018292075959-s0004-0000000149248196-0124-s_lc.fits 
This is the light curve in fits format. So you need a fits viewer to do anything with it or you need to import it into your own (python) code using something that reads fits files. To get started I would download a java program called topcat. This is free and works on windows, linux or mac.
Load the light curve file into topcat. Plot "SAP_FLUX" against "TIME" and that is your basic lightcurve (see below). You can zoom in, manipulate the data, fold the data, subtract or add things to the data, lots of cool things. Plus make plots, anotate them, save them in various formats etc.


It took me 15 mins to write this answer while downloading the data and doing those plots. You can do it!