How did the months and days get their names

MONTHS

The months have history in their names, but some were named for their position in the ancient calendar of 10 months. to be named by their positionthe months lost some logic in the name, but not historical.

January.-January is named after the Roman god Janus, who presided over doors and beginnings – appropriately enough, for the beginning of the year.
February.-February is ultimately based on Latin februarius, from februa. In case that’s not helped things become clearer, februa was the name of a purification feast held on the 15th of this month.
March.-As the Oxford English Dictionary notes, ‘In ancient Rome several festivals of Mars took place in March, presumably in preparation for the campaigning season, since Mars was a god of war.
April.-We know that the English word April comes from the Latin Aprillis, the fourth month of the ancient Roman calendar. April was also sometimes called Eastermonab, ‘Easter month’.
May.-The month is connected with the goddess Maia. Maia was daughter of Atlas and mother of Hermes.
June.-June is named after the ancient Roman goddess Juno. June was also once sometimes known as midsummer month.
July.-The first month in the calendar named after a real person, July was named in honour of Julius Caesar after his death in 44 BC, July being the month of his birth.
August.-The month Sextilis (‘sixth’) was renamed after Augustus, the first Roman emperor, who had died six years earlier.
September.-That it comes from the Latin septem, ‘seven’. As with those, the numbering is a bit off now: September was originally the seventh month in an ancient Roman ten-month calendar, which started with March.
October.-Octo is the Latin for ‘eight’, for that ten month calendar. Two months were added to the end of the calendar year around 713 BC, and the beginning of the year was moved to 1 January in 153 BC.
November.-November comes from novem, ‘nine’. November is also, we’re afraid, used ‘with allusion to November’s position at the end of the year. 
December.-December, from decem, ‘ten’. (the name is before the changue :v)


DAYS

The names of the days are in some cases derived from Teutonic deities or, such as in Romance languages, from Roman deities.

Monday.-The name comes from the Anglo-Saxon monandaeg, "the moon's day". This second day was sacred to the goddess of the moon.
Tuesday.-This day was named after the Norse god Tyr. The Romans named this day after their war-god Mars: dies Martis.
Wednesday.-The day named to honor Wodan (Odin). The Romans called it dies Mercurii, after their god Mercury.
Thursday.-The day named after the Norse god Thor. The Romans named this day dies Jovis ("Jove's Day"), after Jove or Jupiter, their most important god.
Friday.-The day in honor of the Norse goddess Frigg. 
In Old High German this day was called frigedag. 
To the Romans this day was sacred to the goddess Venus, and was known as dies veneris.Saturday.-This day was called dies Saturni, "Saturn's Day", by the ancient Romans in honor of Saturn. In Anglo-Saxon: sater daeg.
Sunday.-The name comes from the Latin dies solis, meaning "sun's day": the name of a pagan Roman holiday. It is also called Dominica (Latin), the Day of God. The Romance languages, languages derived from the ancient Latin language (such as French, Spanish, and Italian), retain the root.