Thank you for your question. On August 3, 2015 I answered a question about the differences between say and tell (click here to see the answer), so here I will focus on the similarities and differences between speak and talk.
In general, both speak and talk are used to refer to the act of expressing thoughts with words. Speak and talk can be used interchangeably in sentences like these:
The most common structure with either speak or talk is the verb(speak/talk), possibly followed by to/with + the listener, possibly followed by about + the topic of the speaking or talking. Here is that structure in short form:
SPEAK/TALK + with/to THE LISTENER(optional) + about TOPIC (optional)
Speak is more formal than talk. In a very formal context you may even hear someone use speaks to as an alternative to indicates, as in the example below. Talk to is not used this way.
In addition, talk is more likely to be used to refer to verbal interaction as an extended activity: communication that lasts a long time and covers a variety of topics:
Finally, only speak can be followed by a language:
I hope this helps.