The modern form of 信 consists of words 言 and person 亻/人, the latter lending its sound, and possibly the meaning ‘say’. In earlier forms instead of person acting as phonetic, it had thousand 千 (which itself uses 人 as phonetic) and still earlier heart/mind 心. The earliest form might have been taken as ‘someone who speaks from the heart’ is believable, trustworthy. The meaning of communication may have originated in a trusted envoy. As mnemonic I suggest to take a hint from Ezra Pound .
Mnemonic: Persons that stand by their words can be trusted
In old Chinese, 信 pointed to a word ‘to believe, trust, faithfulness, truth’ → (‘something written entrusted to an envoy’:) ‘letter’.
信 has one of the shortest entries in Henshall (513), hardly more than a dozen words. He states that 信 consists of words 言 and person 亻 and then concludes: ‘A person’s word is something which can be believed and trusted’.  Wieger (73 C) interprets 信 not as descriptive, but as prescriptive: ‘Sincerity: the quality that the 言 words of every man 人 should have.’ (To my modern ear Henshall’s description sounded initially unconvincing, considering that people often lie, so why trust their words. Wieger’s analyses may be a later reinterpretation and a just-so story.)
Research seems to indicate that originally 信 wasn’t a compound ideograph (会意) but had 人 as phonetic element (形声). In fact, in older forms 信 had other phonetics: 千, and even earlier 心. 
So, 人 gave its sound, and (being the character for ‘person’) probably had some semantic connotation (trust exists between persons). However, I was wondering if 人 phonetically expressed relevant meaning as well. Katō & Yamada (103) give ‘申(しん）’ as the meaning that the sound conveys, by which they probably mean ‘to state, declare’.  Considering this, I can’t rule out that 信 expressed both semantically and phonetically something like ‘a man that says his word(s)’ and thereby suggested trust to the Chinese of that time (even modern English has ‘I give you my word’, i.e. ‘I can be trusted’). The oldest shape, with words 言 as signific and heart/mind 心 as phonetic, could (speculatively) have expressed something like ‘someone who speaks from the heart’ → ‘believable, trustworthy’.