The important thing to keep in mind about con is that it is somewhat more versatile than the English "with," so you will run across many cases where con is used that you probably wouldn't use "with" in English.
Here are some of the most common cases where con is used in a way that differs from the use of "with" in English. Note that in many of the examples given, con could be understood to mean "with," but it would be awkward to translate it that way.
With certain verbs: Con is used with various verbs where a different preposition (or none) is used in English. Such usages are unpredictable and need to be learned along with the verbs.
- Es necesario acabar con el escándalo. (It is necessary to put an end to the scandal.)
- Para comer, basta con cinco dólares. (In order to eat, five dollars is enough.)
- El coche chocó con el tren. (The car crashed into the train.)
- Puedo contar con mis amigos. (I can count on my friends.)
- Tengo que enfrentarme con el problema. (I have to face up to the problem.)
- Me espanto con las hormigas. (I am frightened of ants.)
- Muchas veces sueño con la guerra. (I often dream about the war.)
- Quiero tropezar con mi madre or Quiero encontrarme con mi madre. (I want to run into my mother.)
To form phrases that function like adverbs: You can do the same in English with "with" and other prepositions, but it is much more common to do so in Spanish; in some cases, such phrases are used in preference to or instead of synonymous adverbs.
- Habla con intensidad. (He speaks intensely.)
- Me preguntó con cortesía. (He asked me courteously.)
- Vive con felicidad. (She lives happily.)
- Anda con prisa. (She walks fast.)
Indicating conditions: Sometimes when followed by an infinitive or a noun, con can have a variety of translations to indicate some sort of condition being met or not met. Such translations include "if," "despite" and "by."
- Con decirle que no tengo dinero, todo estará bien. (By telling him that I don't have money, everything will be fine.)
- Con todo, no está enferma. (Despite everything, she's not sick.)
- Con correr puedes verla. (If you run you can see her.)
Contractions: When con is followed by the pronoun mí or ti to say "with me" or "with you," the phrase is changed to conmigo or contigo, respectively.
- Ven conmigo. (Come with me.)
- Vendré contigo. (I will come with you.)