A strong password is a string of letters, numbers, and symbols that seem random. Here's an example:
Hj7SD_jUlsJbp8-2hOwwkHbnIO980-aøæ
But these passwords are virtually impossible to remember unless you use some kind of mnemonic system.
Which is easy!
ONE: Choose a saying, children's rhyme, or any phrase. Like "London Bridge Is Falling Down", or "Once More Onto The Breach Dear Friends Once More", and use the first letter of each word (LBIFD or OMOTBDFOM.)
You can use any famous phrase or saying, or any phrase at all. A tip is to use absurd phrases, as they are easier to memorize.
An example:
"The Pink Dog Swallowed The Rat Quickly Before He Went To Bed"
TWO: Add a number and three symbols, for example like this
$_7317OMOTBDFOM£.
The format is:
2 symbols in front, a 4 digit number, a phrase, 1 symbol at the end.
To make the password stronger you can alternate each letter of the phrase like this: first letter upper case, next letter lower case, next letter upper case, and so on.
$_7317OmOtTbDfOm£
Now, to make the password unique for each site you can use the name of the site as a mnemonic tip. Say you're using Gmail. You could identify this by inserting a "g" or "go" - or better: go for either the 3rd, or 7th letter after the first. 3 and 7 are "magical" numbers, so easy to remember.
The first two letters of Gmail is G and M. Three letters after G is J, and seven letters after M is T.
SO: If you want to use two letters to identify "Gmail" in your password, use "J" and "T" - which are the 3rd and 7th letter after the first two letters of the name of the site. Add these two letters somewhere in your password, like this:
$_7317OjtmOtTbDfOm£
Use the same setup for all sites and just switch the two letters around. If you want to make it a little stronger, add two unique numbers as well. Perhaps "Gmail" can make you think about 7 and 13, as G is letter 7 of the alphabet, and M is letter 13. This gives you the number 713.
$_7317Ojt713mOtTbDfOm£
As you can see, it is easy to make a very strong password that you still may remember easily since you use the same setup for all passwords, even though all passwords are unique at the same time. Choose a longer verse, and more numbers and symbols if you want even more security. And for a completely unique password for each site/app - use a different verse/saying for each site/password.