These are the other (in addition to U Verbs) main sort ("conjugation") of Japanese verbs. They always end in -eRU or -iRU.
It is easy to get from the plain form you find in the dictionary to the polite -mas- forms. Just remove the RU and add mas-.
iru 'there is (animate) (plain)' -> 'there is (animate) (polite)', kangaeru 'consider, think (plain) -> kangaemasu 'consider, think (polite)', miru 'see (plain)' -> mimasu 'see (polite)', neru 'sleep, go to bed (plain)' -> 'sleep, go to bed (polite)', okiru 'get up (plain)' -> okimasu 'get up (polite)', taberu 'eat (plain)' -> tabemasu 'eat (polite)'
There are a small number of verbs ending in -eru or -iru which are U Verbs. Watch out for these! Two common ones are hairu 'enter' -> hairimasu and kaeru 'go home' -> kaerimasu.
犬は寝ます。 Inu wa nemasu. 'The dog sleeps.'
父は起きます。 Chichi wa okimasu. 'My father gets up.'
学生は考えます。 Gakusei wa kangaemasu. 'The student(s) think.'
その人は出ます。 Sono hito wa demasu. 'He/She leaves.'
ミルクは入れますか。 Miruku wa iremasu ka. 'Do you take milk?'
間もなくバスが出ます。 Mamonaku basu ga demasu. 'The bus is leaving soon.'
犬 inu 'dog'
父 chichi '(my) father'
学生 gakusei 'student'
間もなく mamonaku 'soon' (lit. "without even a space")
出る deru '(something) leaves'
As it ends in RU, although not, admittedly, eru or iru, let us meet the third and final irregular verb: 来る kuru 'come'. Its masu form is 来ます kimasu.