Do they have to be following you as well?
No, they don't need to be following you to get your tweet, as long as you include their twitter username in the tweet. For example, if you tweet: "@dharmesh is awesome!", then Dharmesh will get your tweet in his @mentions section. However, it won't show up in his twitter stream unless he is following you. If you tweet: "Dharmesh is awesome!", then Dharmesh won't get that tweet unless he is following you, and happens to catch it in his stream.
You can also Direct Message (DM) someone on Twitter, but they must be following you in order to send them a DM. Be careful with how often you DM and what you DM about because you can annoy some people, and they may decide to unfollow you.
Be aware that people like Dharmesh are following thousands of people, so it's easy for your tweet to get lost in their stream. And you may never get a response from them.
You should take a look at Twitter for Business to learn the basics of Twitter and get ideas on how you can leverage it for your startup.
do you then use Twitter to contact them?
I don't think it's a good idea to contact an investor via Twitter, especially if they don't know who you are. You may come off spammy, and have the opposite effect on them. Plus, how convincing can you possibly be in less than 140 characters?
but how can I talk to such people?
The best way to engage people like Dharmesh is to become involved in what they do. For example in Dharmesh's case, you can comment on his blog, comment on Hubspot's blog, and/or become an active member of this site.
To get an investor interested, at a minimum you need:
- A prototype of your idea
- A business plan
If you don't have either of those two, you need to work on them before you contact an investor.