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Unlike most European languages, Japanese has an equivalent to the English present and past continuous tenses ("-ing").
mahoutsukaisamahajuubakuwotata,teimasu. "The wizard is casting a binding spell."
saburinasanhatabeteimashita. "Sabrina was eating."
naniwoshiteirundesuka. "What are you doing?" or "What are they doing?"
The auxiliary verb is always iru, never aru, regardless of whether the subject or topic is animate or not.
There is also a sentence pattern where the emphasis is on the continuing, not the doing:
mahoutsukaisamahatata'tetsuzukemashita. "The wizard continued casting a spell." (Despite all the distracting noise from the assembled ruffians.) tsuzukeru is "continue". It is a group 1 verb.
saburinasanhanuidetsuzukemashita. "Sabrina continued to undress." (She wanted to stop but, caught in the spell, she couldn't.)
mahoutsukaisamahatata'tehajimemashita. "The wizard began to cast a spell." hajimeru is "start". It is a group 1 verb. The emphasis with this pattern is on the act of starting a continuous action.
saburinasanhanuidehajimemashita. "Sabrina began to undress."
mahoutsukaisamahakyuunitata'tedashimashita. "The wizard suddenly started casting the spell." dasu is "suddenly start". kyuuni is an adverb meaning "suddenly". It is a group 1 verb. The emphasis with this pattern is on the act of suddenly and unexpectedly doing something.
saburinasanhatotsuzennuidedashimashita. "Sabrina suddenly started undressing." totsuzen is another adverb meaning "suddenly".
This pattern implies unexpectedness, so cannot normally be used for one's own actions (which, after all, one is expecting). There may be rare exceptions, such as Sabrina's case, where one suddenly finds oneself doing something involuntarily and dasu can be used.
mahoutsukaisamahatata'teowarimashita. "The wizard finished casting the spell." owaru is "finish". It is a group 1 verb. The emphasis with this pattern is on the act of finishing a continuous action.
saburinasanhanuideowarimashita. "Sabrina finished undressing."
mahoutsukaisamahamoutatarimashita. "The wizard has finished casting the spell." mou means "already", and when used with the past tense indicates completeness (the emphasis with this pattern is on the completeness rather than the finishing). It is very easy to confuse with mo, "also".
The past tense negative, ...masendeshita, implies that something has not been attempted, rather than that it is not yet finished.
mahoutsukaisamahamoutatarimashitaka. "Has the wizard finished casting the spell?"
iie.madadesu. "No, not yet."
iie.tatarimasendeshita. "Finished? He didn't even start."