This is one of the weirdest verbs I have come across. The past tense masculine form is лез/полез--which makes absolutely no sense at all.
Some fixed expressions:
лезть на стену - for being in a state of excitement. Figuratively used it is nearly identical to the English phrase "to be climbing the wall(s)"
лезть в драку - to be contentious or bellicose
лезть в петлю - to stick one's neck out (петля means noose in this expression) for someone/something
лезть на глаза - to be annoying to somebody
It is a verb of motion, so remember to use the accusative form of the object(s), not the prepositional.
Present tense
Я лезу
Ты лезешь
Он лезет
Вы лезете
Мы лезем
Они лезут
Past tense
Лез
Лезла
Лезло
Лезли
Imperative
Лезь
Лезьте
Participles
Present active - Лезущий
Present passive - Леземый
Past active - Лезший
Past passive - I really have no fucking clue when anyone would possibly need to describe something as "climbed," or even how this form would be derived from something as weird as Полезть, but I'll just guess and say Полежённый. Someone please correct this.
Present adverbal - Лезя
Past adverbal - Лезши