I have used the Harvey Grammar and Composition book and found it to be a concise book from which to learn English grammar. There were two tiny English Grammar volumes written by Thomas W. Harvey in the 19th century that cover most anything that anyone generally needs to know about grammar. Harvey's Elementary Grammar is a quick survey of the English language.
"These compact volumes cannot be matched for the thoroughness with which they treat every aspect of English grammar." - Mott Media
Yes, these are super compact, yet they are missing the aspect of diagramming. One can learn the basics of grammar simply by reading the book; yet if you like the logic of diagrams, you'll have to add diagramming exercises.
In my opinion an adult can read the book in two hours and catch up on all of his basic grammar lessons. As a matter of fact, the faster that one reads this book, the better he can make the connection that most of grammar is naming the use of a word as it is used in sentence construction.
Truly many of the words in grammar mean the same as they do in everyday life, for example: conjunction, preposition (pre position - before the noun), relative.
A child would need a teacher who has experience with sentence construction. The Answer Key would be super helpful here, too. It's always easier to check the student's work with the answer handy than to have to figure the answer every time.
Once one understands the connection between the names and the use of the words descriptive writing and prescriptive writing (instructions, legalese) is easier.
To wit, remember that the Harvey's Elementary Grammar of old was ONE little 120 page book! A tiny book! The principles of writing and grammar are simple.
If you are looking for the easiest way to teach from English Grammar lessons, this little book is an excellent start. It is also inexpensive to buy, especially since it is frequently available at Amazon as a used book, too.