Integrating IC transceivers on a pcb
You start by looking up the datasheet for the nRF24L01.

In it, you will find all the information about what it takes to use that chip.

You will also find this circuit diagram:



Right under the schematic is a parts list:



That should answer your question about what you need.

And, yes, you must include an antenna.



Virtually every project that involves an IC starts with reading the datasheet.  

You look it up, see what it says about requirements and operating conditions (powersupply voltage and temperature range and all kinds of other stuff.)  Maybe you can't use it because it is only rated down to 0 degrees celsius and you need to use it in an unheated cabin in Antarctica.

You see how you can connect it to the rest of your circuit. (Oh, it uses SPI.  My microprocessor doesn't have a SPI port.  Can I do SPI via bitbanging?)

And, you see what connections it needs to the outside world. ( Oh.  It needs an antenna and a matching network.  Can I integrate a ready made antenna?  What effect will the circuit board material have on the matching network?)

Finally, you have the certification problem that Damien mentioned:  Can you handle all the details well enough that your finished product will make it through the  certification process?



Given the level of your questions ("Do I need an antenna?")  I would doubt your ability to do it well enough to get it certified - that's a tough job, and I know that I (as a hobbyist) couldn't do it. 

If this is for a hobby project - go for it.  You might manage something that works.

If this is a commercial project:  stick to the module, or get assistance from a more experienced engineer to design your own.