We travel from our place to our destination.
We can use a verb of motion etc. + home without a prepositon.
But if home is immediately preceded by a word or phrase, preposition is neccessary.
We can live/stay/work/be etc. at home, at + ... + home, in + ... + home.
But in cannot be followed directly by home.
We arrive in a country or town.
We arrive in or at a village.
We arrive at a small destination.
We travel by car (but in Mike's car), by bus, train, plain, helicopter, etc. and by sea/air.
We can also go by a certain route or by a certain place:
We can walk or go on foot.
We can cycle or go on a bicycle or by bicycle.
We can ride or go on horseback.
We get into a private or public vehicle, or get in (adverb).
We get on a public vehicle, get on (adverb).
But we go on board a boat (=embark).
We get on/onto a horse, camel, bicycle.
We get out of a private or public vehicle, or get out (adverb).
We get off a public vehicle, a horse, bicycle, etc., or get off (adverb).
Get in/into/out/out of can also be used of buildings, institutions, and countries, instead of go, come, return etc. when there is some difficulty in entering or leaving (in and out are used here as adverbs).
at, into, to, etc. are prepositions; along, on are prepositions and adverbs; till is a conjunction.
Get to/reach can be used with any destination:
Get in (in = adverb) can mean "arrive at a destination", is used mainly of trains: