From eleven to ninety-nine, Japanese is more regular than English. There is no word for eleven, twelve or twenty. There is only ten, and what you put in front of it and behind it. Once you see the pattern you can produce every number in this range without learning a single new word.
Rōmaji help
Above ten, add behind
Ten, then the digit. Nothing else changes:
11
じゅういち
jū-ichi
ten one
12
じゅうに
jū-ni
ten two
15
じゅうご
jū-go
ten five
17
じゅうなな
jū-nana
ten seven
19
じゅうきゅう
jū-kyū
ten nine
Why it works
English hides this logic behind irregular words: eleven, twelve, thirteen. Japanese does not hide it at all, so this range is easier than it is in your own language. If you can count to ten you can already count to nineteen.
Multiples of ten, add in front
The digit, then ten:
20
にじゅう
ni-jū
two tens
30
さんじゅう
san-jū
three tens
40
よんじゅう
yon-jū
four tens
70
ななじゅう
nana-jū
seven tens
90
きゅうじゅう
kyū-jū
nine tens
88
はちじゅうはち
hachi-jū-hachi
eight tens eight
Why it works
Both halves at once gives you every number to ninety-nine. 88 is はちじゅうはち, literally eight-ten-eight, and you did not have to learn a word for eighty. Note that 40, 70 and 90 use よん, なな and きゅう here, which is the day one rule holding.
The two mistakes people make
Both come from translating English word order:
Twenty
Not this
じゅうに
jū-ni
This
にじゅう
ni-jū
じゅうに is twelve. にじゅう is twenty. The order is the whole meaning, and getting it backwards is the classic slip.
One hundred
Not this
いちじゅうじゅう
ichi-jū-jū
This
ひゃく
hyaku
The pattern stops at 99. A hundred is its own word, which is day three.
Why it works
The first pair is worth drilling until it is automatic, because in a shop the difference between twelve and twenty is real money. A useful trick while you are learning: say the number in English in Japanese order first. Twenty is two-ten, twelve is ten-two. Then the Japanese falls out on its own.