This is a lot easier than it seems at first, largely because our (Roman) alphabet is directly descended from the Greek.

First, as anyone who has looked over Greek letters can see, many of them closely resemble ours. Indeed, many are virtually identical, especially the vowels. The following Greek letters look like and sound like their modern counterparts:

α, β, ε, ι, κ, ο, τ, υ – Eight letters, so close that I’m not even going to define them.

Next are several letter whose form is so close to their English equivalent that they are easily recognized:

δ – delta, like our ‘d’
γ – gamma, like ‘g’
λ – lambda, like ‘l’
μ – mu, like ‘m’ (Compare to a script ‘m.’)
ν – nu, like ‘n’ (Sure, it might look more like a ‘v.’)
ς,σ – sigma, like ‘s’ (two forms, ς at the end of words, σ in the middle)
ω – omega, with an ‘aw’ sound

Then are a few letters whose shapes seem odd, but correspond directly to English letters:

π – pi, like our ‘p’ and π = 3.1415926, as everyone knows anyway
ρ – rho, like our ‘r’ (which does look more like a ‘p’)
ξ – xi, ‘x’ sound
ζ – zeta, ‘z’ sound

Thus, we are left with a few tricky ones, mostly consonant combinations:

η – eta, a vowel, sounds like ‘eh’
θ – theta, ‘th’ sound
φ – phi, ‘f’ sound
ψ – psi, ‘ps’ sound
χ – chi, hard ‘ch’ sound (or like a ‘k,’ but not like x’)

So, that’s all 24, re-capped here, in alphabetical order:

α – alpha
β – beta
γ – gamma
δ – delta
ε – epsilon

ζ – zeta
η – eta
θ – theta

ι – iota
κ – kappa
λ – lambda
μ – mu
ν – nu
ξ – xi
ο – omicron
π – pi
ρ – rho
σ,ς – sigma
τ – tau
υ – upsilon

φ – phi
ψ – psi
χ – chi

ω – omega

I broke them up into several groups, to help memorize them. Note that the first five match ABCDE very closely and that the other long group matches our letters I.KLMN.OP.RSTU closely (omitting the unommon “J” and “Q” and inserting xi in an odd place).

Then there are two little groups of rhyming letters “zeta, eta, theta,” and “phi, psi, chi.” (Think of ‘phi’ as sounding like ‘v’ – it does, and it IS related)

Of course, as in the phrase “from the alpha to the omega,” the letter ‘omega’ comes at the end.

The history of the alphabet, from Semitic letters, through Greek capitals, through Latin letters, and some changes in Medieval times, further helps to learn the Greek alphabet. These things are not just arbitrary constructs invented by boney-fingered crones who teach grammar in seventh grade. They evolved naturally, in response to people’s need to communicate.