Dylan Thomas's poem "Do Not Go Gentle into that Good Night" is written in a poetry structure called a villanelle. In the Renaissance period, a villanella, called a villancico in Spanish and a villanelle in French, was an Italian and Spanish dance-song. As a dance-song, a villanelle has a very specific structure; a villanelle also typically contains pastoral or rural themes.
First, a villanelle has a 19-line structure, as we can see in Thomas's poem. Second a villanelle, like a sonnet, is also written in iambic pentameter. A line of iambic pentameter is made up of 5 feet, also called iambs. An iamb is made up of two syllables, a short syllable followed by a long syllable; we can also call such syllables unstressed and stressed. Another way to phrase this is that a line of iambic pentameter follows a da-DUM da-DUM da-DUM da-DUM da-DUM pattern. Hence, as we can see, a line of iambic pentameter will contain a total of 10 syllables broken into 5 feet.
We can see an example of iambic pentameter in the very first line of Thomas's poem:
Do not go gentle into that good night
In the above, words in boldface represent the stressed syllables, showing us that the line contains a total of 5 feet and 10 syllables, making it a perfect example of iambic pentameter.
To continue discovering the number of feet, we can first multiply the 5 feet in each line by the number of lines, which is 19, to get 95 feet. We can then verify this number by continuing to count the number of syllables in each line, which should be 10. Counting is a good idea because there can always be some variations in meter. We see one variation in the following line of the 5th stanza, which has 11 syllables:
Blind eyes could blaze like meteors and be gay
However, it is possible to compress the three-syllable word meteors into two syllables when speaking it, which would still be consistent with our iambic pentameter, as follows:
Blind eyes could blaze like mete-ors and be gay.
Hence, as we can, the total of feet in the poem is 95.