how to improve at chess

That's a rather broad question, and you'll find plenty of other threads out there answering the question.

Basically, by playing games of chess. Study. Analyse your own games. Do lots and lots of tactics. Do lots and lots more tactics.

Possibly of interest:
Simple Attacking Plans by Fred Wilson (2012)
https://web.archive.org/web/20140708090402/http://www.chesscafe.com/text/review874.pdf
http://dev.jeremysilman.com/shop/pc/Simple-Attacking-Plans-77p3731.htm
Logical Chess: Move by Move by Irving Chernev (1957)
https://web.archive.org/web/20140708104437/http://www.chesscafe.com/text/logichess.pdf
The Most Instructive Games of Chess Ever Played by Irving Chernev (1965)
https://chessbookreviews.wordpress.com/tag/most-instructive-games-of-chess-ever-played/
Winning Chess by Irving Chernev and Fred Reinfeld (1949)
https://web.archive.org/web/20140708093415/http://www.chesscafe.com/text/review919.pdf
Back to Basics: Tactics by Dan Heisman (2007)
https://web.archive.org/web/20140708233537/http://www.chesscafe.com/text/review585.pdf
https://www.chess.com/article/view/book-review-back-to-basics-tactics
Discovering Chess Openings by GM John Emms (2006)
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
Openings for Amateurs by Pete Tamburro (2014)
http://kenilworthian.blogspot.com/2014/05/review-of-pete-tamburros-openings-for.html
https://chessbookreviews.wordpress.com/tag/openings-for-amateurs/
https://www.mongoosepress.com/catalog/excerpts/openings_amateurs.pdf
Chess Endgames for Kids by Karsten Müller (2015)
https://chessbookreviews.wordpress.com/tag/chess-endgames-for-kids/
http://www.gambitbooks.com/pdfs/Chess_Endgames_for_Kids.pdf
A Guide to Chess Improvement by Dan Heisman (2010)
https://web.archive.org/web/20140708105628/http://www.chesscafe.com/text/review781.pdf
Seirawan stuff:
http://seagaard.dk/review/eng/bo_beginner/ev_winning_chess.asp?KATID=BO&ID=BO-Beginner
https://web.archive.org/web/20140708092617/http://www.chesscafe.com/text/review560.pdf
https://www.chess.com/article/view/book-review-winning-chess-endings
https://web.archive.org/web/20140627132508/http://www.chesscafe.com/text/hansen173.pdf
http://www.nystar.com/tamarkin/review1.htm

Reading chess books helps: http://chesswinning.com/7-best-chess-books/

Also, analyzing grandmaster games can be very useful at times as well. Here's how to do it: http://chesswinning.com/how-to-analyze-chess-games/