Simple exercises? I'd recommend this forum for practice with calculations with pieces https://www.chess.com/forum/view/game-analysis/calculation-training
and I recommend "vision trainer" on chess.com for board visualization. ("vision trainer" is one the chess.com "learn" part of the sidebar, just above "analysis" [titled "vision"]).
There are a few other things you can do to train this ability, but they are more long term. One thing I recommend is attempting puzzles and tactics without moving any pieces until you think you see the entire sequence in your head. Yes, you will get more puzzle incorrect - but it will help you with your long term calculation ability. If you don't want to try this method for fear of your tactics rating dropping, then play unrated chess.com tactics.
Feel free to message me for other ideas too (or to let me know which ones you might be willing to try if you want to share) 
I have a goal to learn to play blindfold chess. But first things first, I need to be able to visualize better even looking at the board and pieces. When I play "daily" I can use the analysis board to test my theories, but in Rapid or OTB, etc, I am playing by the seat of my pants...there isn't really some deep visualization of candidate moves...mostly intuition, and as you can see from my rapid rating, I could stand much needed improvement.
When I do tactics, I am pretty good at solving puzzles, but I can find the first couple moves and then when the computer makes the response to my moves, I figure out the next moves. I can not visualize well or clearly.
Through some tricks I can name the colors of the squares, but picturing a board, or a board with pieces is blurry in my mind. I need to flex this muscle to get better.
Does anyone here know of any simple exersizes to improve visualization with the short term goal of using it in over board and timed games, and with the long term goal of playing a whole game blindfolded.