It goes without saying, but the point of contact between people is 'words.' Through those words, we share our thoughts and carry on discussions.

Literal

Obvious is-[though-だが], person [and-と] person [and-との] contact-point [topic-は] 'words' are. Those words [by-によって], thoughts [obj-を] share-[and-し], are-discussing.

あたりまえだが is a discourse opener 'obvious as it is, but...' — setting up something the speaker knows is cliché before making an essay-style observation. 人と人との is a nested possessive: 人と人と (two people) + の (attributive), turning 'person-and-person' into an attribute of 接点 ('contact point'). で+ある is the formal copula, more elevated than plain だ. ~によって marks the means. The two-clause second sentence uses し to parallel 共有する and 議論している. Formal, essay-style.