Despite what you might read in certain online forums, you should almost always speak to (or talk to) someone and not speak with (or talk with) them.
Broadcasters seem to favour the latter, but it is important to understand the reasoning behind the distinction because it is not simple pedantry.
If you are speaking with someone, it insinuates that you are both speaking at the same time – and that’s usually not conducive to clear communication.
However, if you are speaking to someone, it implies that you both will take turns in the conversation or interview.
A (precise) exception helps demonstrates a subtle difference. It is correct to say:
“He will be speaking with nine other speakers at the conference.”
This means he is just one of 10 speakers to address the conference.
It is also correct to say (but the meaning is definitely altered):
“He will be speaking to nine other speakers at the conference.”
This means he will have conversations with nine conference speakers, but it is now unclear whether he is a speaker as well.
Still not convinced?
If you are talking with someone, it also implies that you are both speaking simultaneously.
But if you are talking to someone, it suggests you are politely taking turns to speak.
Perhaps the confusion has arisen from a hesitance about the pejorative use of speak to or talk to when suggesting more of a one-way encounter, as in:
A teacher saying to a student: “Come and see me after class because I want to speak to you.”
A frustrated parent saying to a naughty child: “You need a good talking to.”
This is one occasion, however, when too much politeness muddies meaning.
If you like what you’ve read here, you can see reporting4work’s similar posts at Style Matters