Opened in 1923, the stadium, known from 1923-80 and again since 2008 as the Eintracht Stadion, has a capacity of just over 23,000. It is owned by the City of Braunschweig and, in addition to football, also stages athletics meetings and American football games.

Various modifications post WWII and during the early years of the Bundesliga (launched in 1963) took the capacity up to around 40,000 by the time Eintracht Braunschweig clinched the league title with a 4-1 win at the stadium over 1. FC Nuremberg in 1967.

Prior to that momentous match, the stadium had hosted the final of the German FA Cup (DFB Pokal) in 1955. It has also hosted the American football 'German Bowl' and 'Eurobowl' on multiple occasions since 1995, and the German Athletics Championships many times since the turn of the century.

Modernisation and the installation of seating to replace old terraces have reduced the capacity to its current 23k-ish, but the Südkurve (South Curve) remains terracing (for around 95.k home fans) and the northwest corner of the ground also includes terracing for away fans.

I've posted a collection of photos here.

Getting there from the city centre
As shown in my collection of photos (see link above), there is a shuttle bus service on match days from right outside the main station straight to the ground. There is also a tram hub outside the station, from which the M1 and M2 services run to the stadium. The M1 stops at the 'Stadion' stop and shows 'Wenden' as its destination, while the M2 stops near the stadium at the 'Gesundheitsamt' stop and has 'Siegrfriedviertel' as its destination. On match days, extra trams run to the stadium as the 1E. All three services run through the city centre, so you can also get on there.

Eintracht Braunschweig match tickets double as tickets for the local buses and trams on match days. They are valid in Tarifzone 40 (zone map here as PDF) from 3 hours before the game until the services stop running that night.

Depending on the length of your planned stay in the city/Germany, it might be worth you getting a Deutschlandticket for unlimited use of local and regional public transport throughout the country.  

If you are flying in for the game from the UK, the nearest international airport is Hannover Airport.