Best way to visit Reichstag

You only need to book a reservation online to visit the Reichstag dome.
No ticket, it's free.
Rick explains the procedure in depth in the Germany guidebook. Very easy to follow.

We did the official guided tour last August and it was interesting and informative and you do skip the line. The tour itself took more than 90mins (we had a very chatty group that asked a lot of questions) then we stayed in the dome on our own for about 30mins. The tour mostly covered the history of the building. You also get to enter the main hall of the parliament where debates occur etc. If you have a limited amount of time, I would skip the tour and just do the dome.

You cannot visit inside the Reichstag without a reservation for the guided tour. The people who choose to visit the dome only do not get to see inside the Reichstag (apart from the dome). They take the elevator straight up to the dome.

You can reserve the dome "tickets" in advance on their website. You can visit the dome without reserving "tickets" early BUT you will have to line up for tickets on the day of. When we were there the dome ticket lines were 3 hours long!!!
There is no charge to reserve a slot for the dome or the tour.

This is the website we used to reserve our tour slot. You can also use it to reserve your dome visit slot.
https://visite.bundestag.de/BAPWeb/pages/createBookingRequest.jsf?lang=en

I took the Reichstag tour twice, in May 2013 and March 2014. In both cases, obtained an entry time on line well in advance. Both tours started in the same location -- a sitting area around the corner from a hallway whose walls were covered with the writing of Russian soldiers who occupied the building in May 1945. In May 2013, the guide took us directly to the legislative chamber; in May 2014, the guide took us into that back hallway and translated some of the writing (including one note from a soldier from Stalingrad who essentially said this is payback). Next, we went to the main legislative chamber, located directly under the dome, for a 20-30 minute overview of the history of the building, the German government/legislative process/German role in the EU, and other topics. Following that session, the two tours diverged; in May 2013, the guide took us one flight down and through a long hallway and into an adjoining futuristic office complex, while in March 2014, the guide took us into a private second floor library with a balcony overlooking the Spree River. We then exited the library and walked directly past Angela Merkel's office. Both tours ended with a trip on our own to the dome, which included a free audioguide. In the dome, there is also a display that chronicles the history of the building. So, if you are interested in learning about the German government, seeing where the legislators meet, and getting a behind the scenes look, then the tour is highly recommended. Alternately, if you just want to do the dome, that would be much quicker and you can read the displays and then ascend the spiral walkway, listening to the audioguide. Berlin is a huge city, so if you are going to the Reichstag, I would leave the sites in the West (Ku-dam, the Zoo, Charlottenburg Palace, Kaiser Wilhelm Memorial Church) for another visit and initially concentrate in the area of the Reichstag and Brandenburg Gate. You are within walking distance of a plethora of sites (Memorial to the Murdered Jews of Europe, Potsdamer Platz, Topography of Terror, site of Hitler's bunker, Checkpoint Charlie, Gendarmenmarkt, Fassbender & Rausch Chocolatier, etc.), and then could eventually work you way back to Unter den Linden and head towards the Museum Island and Alexanderplatz. If you would want to see the best preserved remnant of the Berlin Wall, then head north towards the Bernauerstrasse memorial. You could catch dinner in Prenzlauerberg. Rick has a self-guided tours of Berlin in his Germany book and in his Audio Europe app.