"We talked about a lot of things."
It's difficult to put these in simple words. However, I am going to give you the brief description of each.
1) 讲 literally means "to speak with", which is used to express a single person speaking instead of one. This can be used casually.
2) 说 means "to say". Here, 说 is interchangeable with 讲. However, it refers to multiple people in the conversation, where they express opinions toward the specific topic or subject.
3) 谈 actually means "to discuss", which stresses some depth of the topic currently brought up.
Just some examples for NasuSamaruk0's explanation:
1) 讲 has a more preach/explain/formal/informative/one-sided kind of meaning to it, usually not used alone but in a phrase （讲道理，讲究，讲解） for example:
领导在讲话 The leader/boss is giving a speech OR The leader/boss is talking.
她在讲故事 She is telling a story
导游在讲解 The tour guide is guiding/explaining
2) 说 can be used alone, and is the most common:
她说：“好的” She said: "ok."（using 讲 or 谈 would not be proper here）
你说什么？(What did you say?)
她在说话 She is talking （not a speech/presentation）
3) 谈 usually involves a discussion.
领导找我谈话 The boss wants to have a talk with me
我们谈到了她 She was mentioned in our talk / We brought her up during our conversation.
The examples seem correctly sound to me. 讲 and 说 have the closest meanings to each other and are two of the most commonly used verbs, but to different extents of meaning. The usages of hanzis are very nuanced throughout as you encounter any Chinese language, so you might want to treat them as if they are interchangeable.
I will add few details about few sentences:
- If the text were to appear on the book, 她说：“好的” is equivalent to 她：好的.
- 你说什么？ appears more than 你讲什么？
I would also want to share few more bonuses, involving these verbs and complex meanings. For instance,
- 談何容易 It's easy to say [than to do]; this is the popular 成語 (Chengyu) used both in classical and modern Chinese eras.
- 說三道四 literally means "say-three direction-four", which figuratively means "to say something thoughtless". If you look at the contrasting numbers 三 and 四 carefully, then you should notice how well-contrasted the clauses are.
I prefer traditional Chinese (since there are meanings behind radicals in the characters), but I can also write and read simplified Chinese.