If you ever need to transliterate chunks of Greek to roman letters, there’s a web tool for that at lexilogos. You type or paste your Greek into one box and the transliterated version appears in another.
If you need to type some Greek and for some reason cannot activate or install an input system on the computer (or if typing Greek is not something you plan to do again), you can try this online “keyboard” from Lexilogos. When you click a pictured letter (including letters with diacritics), it appears in the text box. The letters highlight as you hover over them, so it’s easy to see which you’re clicking. When you’re done, just copy the text and paste it wherever you want.
Greek – LSJ, Middle Liddell, Autenrieth’s Homeric Lexicon, Slater’s Lexicon to Pindar
Greek can be entered as Unicode Greek; you need not (but may) include diacritics. You can also use transliteration, so that entering at least “mhn” will suggest “μῆνις” [edited to reflect Helma Dik’s helpful comment].
Latin – Lewis and Short, Lewis’s Elementary Latin Dictionary, Frieze-Dennison Vergil, etc.
Greek – LSJ (also Autenrieth’s Homeric Lexicon, experimentally)
Note that you must enter your search terms for Greek in BetaCode (manual here), but you can (and should, for most purposes) choose to have the output in Unicode.
Latin – Lewis and Short
Other dictionaries available for Arabic, Sumerian, etc.
The Bridge creates a custom vocabulary list by comparing the words that you (or your students) know to the words in a text that you want to read.