A good place to study and practice is musictheory.net - it's got a lot of helpful resources.
The biggest thing is knowing the relationships of scale degrees to chords.
Your basic major triad is 1-3-5 all diatonic to the key, example C the I(1) chord is C-E-G, now for the different variations of 7th's you have the Maj7 (natural 7 in the key) B, half step away from the tonic of C (leading tone), you have the b7 for a C7 Dom7th chord which is B flat, and then you can have a diminished 7th chord as well where its minor 3rds stacked on top of each other, so C Eb Gb Bbb(A), and obviously don't forget the Minor 7th Chord, which is C Eb G Bb.
So Major 7 - 1-3-5-7
Dom 7 - 1-3-5-b7
Minor 7 - 1-b3-5-b7
Half Dim 7 - 1-b3-b7-b7 (also known as minor 7 b5)
Dim 7 - 1-b3-b5-bb7
I'm sure I goofed up some wording here, but I think it's correct for the most part I'm kind of hurrying through the day but wanted to chime in.
The other extensions you have are 9/#/b(2),11/#(4),13/b(6), there are also 6th subs and b5's, as well as #5's, sometimes I've seen 10ths used as well, notice all the (common) extensions are the scale degree +7 aka up an octave, which is not always the case, extensions can be in a huge variety of ways and are not always on the top.
So my advice, start with understanding triads and knowing in Major Keys, your chords are
I(major),
ii(minor),
iii(minor),
IV(major),
V(major also often known as V7 dominant chord),
vi(minor),
viio(diminished).
In minor keys
i(minor)
iio(diminished)
III(major)
iv(minor
V/v(technically diatonically it's minor but I can't think of any minor v in modern popular music doesn't mean the aren't there, its usually assumed major)
VI(major)
VII(Major)
Notice the in the relative major to minor relationship the i=vi, iio=viio, III=I, iv=ii, V=iii(kind of if it were minor?), VI=IV, VII=V and vise versa, I started with the minor to major, just flip it around for major to minor. Example A is the 6th scale degree in C major, also known as the relative minor aka Aeolian mode, and the minor vi chord.
I'm sure more people will chyme in but hopefully this will give you a basic start.
Dallas