I believe it was CJS Purdy who stated that you need to look at "All checks and captures" before you even begin to analyse your likely moves. While such advice seems obvious, it's simplicity makes it easy for players to ignore. Many a game has been lost in the rush of excitement when your opponent plays an unexpected check.
One simple training exercise is to choose a game and start to play through it. The first time you play through it, simply list all the checks and captures that can be played on the move. Do this for the whole game. Once you have played through a few games and are confident you aren't missing anything, move onto the next level.
The next level consists of visualising the next move, but don't play it on the board. Then list all the checks and captures that can be played in reply to the game move. Again, do it for a number of games, until you feel confident.
Then once you've mastered that you can extend to 2,3 4 or more half-moves ahead. In doing this exercise you develop two skills. Firstly you improve your visualisation skills by keeping a new position in your head, and secondly, you develop your tactical awareness.
If you need a game to give you a kick start here is one between Vasilly Smyslov and a very young Boris Spassky
Smyslov - Spassky [B76]
clock simul Soviet Union, 1948
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.f3 0-0 8.Qd2 Nc6 9.0-0-0 Nxd4 10.Bxd4 Qa5 11.Bc4 Rd8 12.Kb1 Be6 13.Bxe6 fxe6 14.h4 Rac8 15.h5 b5 16.hxg6 hxg6 17.Qg5 e5 (D)
For example, in the diagrammed position White has 1 check (Rh8+) and 6 captures (Qxg6, Qxf6, Qxe5, Bxe5, Bxa7, and Nxb5). If you were looking 1 half move ahead (after White plays Qxg6) you would see that Black has 1 check (Qxa2+) and 5 captures (Qxa2, Qxc3, Rxc3, exd4 and Nxe4)
18.Qxg6 exd4 19.Nd5 Rd7 20.Rh3 Qd8 21.Rdh1 1-0