Question: I'm not into physics so I don't know the exact wording for this kind of things, but I do my best:

I would like to have a device which generates frequencies. These frequencies should be directed to a antenna or something similar. Is this possible to build on a home-made-basis?

Thanks in advance :-)

Kind regards,
Max

Answer: 
I am assuming you are talking about transmitting a carrier frequency. Then you basically have a lot of choices: depending on the range of frequencies (e.g FM, AM, etc). 

If you are interested in FM frequencies, this link does a pretty good job describing how you'd build one (<https://www.instructables.com/id/How-to-Make-FM-Transmitter/>).
What you want is called a *radio frequency signal generator*. These are tuneable across broad ranges of frequencies but usually come in several different models depending on which segment of the RF spectrum you wish to work in: low frequency (less than 500 kilohertz), medium frequency (500 kilohertz to 2 megahertz), high frequency (2 megahertz to 50 megahertz) very high frequency (50 to 150 megahertz), ultrahigh frequency (150 to 500 megahertz) are the common ranges.

These will produce an RF signal that, when connected to an antenna, will transmit a (weak) signal over a distance of several feet. 

To get more range, you will need an *RF power amplifier*, but for that you will also need to be licensed by the FCC.