I'm just learning this myself, but from what I've learned it's a little more subtle than that. If the word starts with a vowel or a plosive consonant, it's τον (masculine) or την (feminine). Otherwise, it's το (masculine) or τη (feminine).
The plosive consonants are the ones where you block a part of your mouth to completely stop airflow: B, D, G, K, P, and T.
Β is μπ (not β)
D is ντ (not δ) (also τζ which is DZ)
G is γκ (not γ)
K is κ (also ξ which is KS)
P is π (also ψ which is PS)
Τ is τ (also τσ which is TS)
So it's τον/την if the word starts with a plosive consonant (μπ, ντ, γκ, κ, ξ, π, ψ, τ) or any vowel (α, ε, ι, η, ο, ω, υ). Otherwise, it's το/τη.
Βλέπω τον άντρα. (I see the man.) - masculine, starts with α, so it's τον
Βλέπω το δρόμο. (I see the road.) - masculine, starts with δ, so it's το
Βλέπω την κότα. (I see the hen.) - feminine, starts with κ, so it's την
Βλέπω τη γυναίκα. (I see the woman.) - feminine, starts with γ, so it's τη
This also extends to στον/στο and στην/στη for indirect objects, since these words are just a contraction of σε and the appropriate accusative article.
Note that the definite article is always το for neuter (because neuter articles and nouns never change forms in the accusative, only masculine and feminine ones do).
Anyway, this is my understanding. I'm new to this so I'm sure a native Greek speaker can point out if I have made a mistake or left anything out.
SassanSanei, your explanation is absolutely perfect (Native speaker here)! It really should be included in the tips and notes. But then, maybe it's good to have some extra reward for those who don't skip the comments!
Just one remark: when (σ)το/(σ)τη is used (not vowel or plosive consonant), you may also add the ν. When (σ)τον/(σ)την is used (vowel or plosive consonant), you can't omit the ν. So:
- Βλέπω το δρόμο or τον δρόμο: both correct
- Βλέπω την κότα: correct, τη κότα: wrong