It’s a one. When deciding whether to use “a” or “an”, you want to choose based on the sound the word begins with, not the actual letter it begins with. Since “one” starts with a “w” sound, “a one” is the right one.
It’s a European. The rule for using “a” or “an” is based on pronunciation of the word that follows, not the spelling. The first sound of the word European (and Europe) is consonant (you).
“A euro” is the correct one. The rule for using “a” or “an” is based on pronunciation, not spelling. Since “euro” begins with a consonant sound (it is pronounced “youroh”), we use the indefinite article “a”.
It’s “a euphony”. Use “a” (instead of “an”) if the following word starts with a consonant sound. The word euphony, despite starting with a vowel, makes a “you” sound.
It’s a euphemism. The rule for using “a” or “an” is based on pronunciation, not spelling. Since “euphemism” starts with a consonant sound ("you" sound), we say “a euphemism”.
We typically use the article “the” to introduce a range of leisure activities and forms of entertainment (e.g., “to the beach”, “to the mountains”, “to the movies”, “to the disco”, “to the opera”, etc.).