The basic meaning of com is with. However there is no guarantee that com is used when it would be very obvious to use it. Escrever com lapiz, to write with a pencil, would be obvious. However it is escrever a lapiz. At the other side sometimes with is used where we don't expect it at all. In Portuguese people are not surprised about something, but surprised with something, ficar sorpendido com.
The disjunctive pronouns mim / te / nos / vos / si + com become comigo, contigo, connosco, convosco, see 6.1.4.
In Portuguese very often we find a construction with com + noun where we construct with an adverb in English. This can be due to stylistic reasons or to the fact that there is no corresponding adverb.
com + noun for English adverb
O euro foi aceite, e até recebido com entusiasmo, por muitos cidadãos.
The euro was accepted and even received enthousiastically by many people.
A situação tem evoluído no bom sentido mas com demasiada lentidão.
The situation developed in the right direction, but too slowly.
É com muito gosto que respondo à sua pergunta.
I am very happy to answar your questions.
Disseram que tinham provas, mas não sei com certeza.
They said that they have proofs, but I am not sure.
In most cases however it is possible to translate with the corresponding English preposition.
Saiu com os amigos.
He has gone away with his friends.
Ela saiu assim que falou convosco.
She has gone soon immediately after having spoken with you.
Estamos confrontados com um fenómeno global.
We are dealing with a global problem.
Estou disposto a debatê-lo convosco.
I am willing to discuss this issue with you.
A interação com nossos clientes é baseada na confiança.
The relationship with our customers is based on trust.
Teria sido agradável falar com ele pessoalmente.
It would have been nice to discuss about it with you personally.
Homens representam 53% dos internautas com intenção de compra.
53 percent of the internet user with purchase intention are men.
Não vai estar conosco* para sempre.
She will not always stay with us.
* com + mim => comigo, com + ti => contigo, com + ele / ela / se => consigo, com + nós => conosco, com + vós => convosco, com + eles, elas, se => consigo
Sometimes the structure of the sentence has to be changed completely
com not translated at all
Regressou para se casar comigo.
He came back to marry me.
Sometimes in English a completely different preposition is used.
O que aprendi contigo, no entanto, tem um valor especial.
All what I have learnde from you has a special value.