This is the greek alphabet:
Α α Alpha Β β Beta Γ γ Gamma Δ δ Delta Ε ε Epsilon Ζ ζ Zeta Η η Eta Θ θ Theta Ι ι Iota Κ κ Kappa Λ λ Lambda Μ μ Mu Ν ν Nu Ξ ξ Xi Ο ο Omicron Π π Pi Ρ ρ Rho Σ σ Sigma Τ τ Tau Υ υ Upsilon Φ φ Phi Χ χ Chi Ψ ψ Psi Ω ω Omega
Just look up "Greek keyboard" on an internet search engine (Google being the usual one), save the image, open it up, place the internet window on one side and the image on the other, and that way you just look at the image in one window, and then type in the internet window (of course...if you use "windows" :) ).
How do I know when to use "η" instead of "ε" and vice versa?
Eh? They sound quite different: η sounds like English "long E" as in "meat", while ε sounds like English "short E" as in "met".
So η sounds like ι ει οι υ, and ε sounds like αι. When to use each of those is something you simply have to memorise -- like how you have to memorise when to use ee or ea in English words such as "meet" and "meat".