How to Solve Tactics

I'm not going to get into the reasons why you should study tactics if you're around my level. I've read enough to convince myself but here's one of the first sources I read that did the job:

http://www.masschess.org/Chess_Horizons/Articles/2001-01_Sample_400_Points_Part_1.pdf
http://www.masschess.org/Chess_Horizons/Articles/2001-04_Sample_400_Points_Part_2.pdf

Strategy vs Tactics
Long-term strategic moves are very hard for the beginner to understand (something I need to start working on!) but tactics can be seen pretty much immediately because of the forcing nature of the replies. Here's an example of explaining a strategic move versus a tactical move:

STRATEGIC: You'll want your rook on b8 because the pawn structure you developed is begging for a minority attack. First you'll need to prep a knight maneuver and before that you need the rook on b8. After the minority attack is initiated, the b-file will likely be opened in the middlegame and the b8 rook will come alive!

TACTICAL: You take here, your opponent has to take back otherwise they're losing a bishop, then when he takes back, you can take on e5 which is also a fork and you'll win you two pawns!

A Guide to Solve Tactics
There often aren't guidelines provided to a beginner on what to look for when doing tactics training. "Look for checks and captures" is good advice to start but it doesn't apply to a whole lot of puzzles. I got some helpful advice from a redditor who told me a "structured approach" to tactical problems is extremely helpful to familiarize yourself with what's going on in the position and figure out where on the board to attack.

Generally, any of three elements may be present in most tactics puzzles. Knowing what these are and being able to spot them quickly is a great head start in solving tactics. By "elements" I don't mean pins or forks, I am talking in broader terms.

The three elements:

1. Un(der)defended Pieces - Pieces with the same amount of attackers as defenders. The remedy: Either remove the guard [by some other tactical mechanism or by exchange] OR add a marginal attacker

2. Favorable Geometry - Important or undefended squares on the same diagonal or file, or on squares that can be forked by a knight or pawn. Remedy: pin/fork/skewer!

3. Trapped Pieces - Pieces on awkward squares or with little to no available mobility. Remedy: Attack it with a piece of lower value OR add a marginal attacker

​For a tactic to work, typically there must be at least 2 of these elements present.

I will hopefully later add some screenshots describing the elements in more detail.

If you can take any tactics puzzle and list out the underdefended pieces, all instances of favorable geometry, and any trapped pieces, you will be well on your way to knowing where to start calculating. As you train tactics more and more, you'll start to find yourself spotting these elements very quickly and intuitively knowing which ones to start calculating. For calculating, it can be helpful to go through all checks, captures, and then threats with a priority of checking the highest value pieces first.