The main connections you should know

Trams

Tram 1: Neuberesinchen <-> Stadion
– leaves Neuberesinchen at ’09, ’29 and ’49 and at ’04, ’34 on weekends, holidays
– reaches Bahnhof in 10 minutes
– connection to tram 4 at Dresdener Platz (and both tram 1 and 4 in the other direction with a short wait)
– connection to tram 2 at Zentrum
– connection to 983 (Slubice) at Zentrum [!] Once in an hour
– [!] Zentrum is not a connection point between tram 1 and 4!

Tram 2: Europa-Universität <-> Messegelände
– leaves Europa-Universität at ’00, ’20 and ’40 and at ’15, ’45 on weekends, holidays
– leaves Westkreutz at ’04, ’24 and ’44 and at ’27, ’57 on weekends, holidays (towards Europa-Universität)
– leaves Witzlebenstraße at ’07, ’27 and ’47 and at ’32, ’02 on weekends, holidays (towards Europa-Universität)
– connection to tram 1 at Zentrum
– connection to tram 4 at Zentrum
– connection to 983 (Slubice) at Zentrum [!] Once in an hour

Tram 3: Europa-Universität <-> Markendorf (Ort)
– leaves Europa-Universität at ’03, ’23 and ’43 and at ’25 on weekends and at ’50 during school breaks
– connection to tram 5 at Dresdener Platz (and to tram 1, 4 with a 10 minute wait)

Tram 4: Markendorf (Ort) <-> Lebuser Vorstadt
– leaves Dredener Platz at ’17, ’37 and ’57 and at ’12, ’42 on weekends, holidays (towards Lebuser Vorstadt)
– leaves Magistrale at ’13, ’33 and ’53 and at ’08, ’38 on weekends, holidays (towards Markendorf (Ort))
– connection to tram 1 at Dresdener Platz
– connection to tram 2 at Zentrum
– connection to 983 (Slubice) at Zentrum [!] Once in an hour
– good for going to Slubice, change at Dresdener Platz, get down (or board) from Magistrale and walk to Slubice
– [!] Zentrum is not a connection point between tram 1 and 4!

Tram 5: Neuberesinchen <-> Messegelände
– leaves Neuberesinchen at ’18, ’38 and ’58 and does not run during holidays or during school breaks.
– leaves Westkreuz at ’18, ’38 and ’58 and does not run during holidays or during school breaks. (towards Neuberesinchen)
– leaves Witzlebenstraße at ’15, ’35 and ’55 and does not run during holidays or during school breaks. (towards Neuberesinchen)
– connects to tram 3 at Dresdener Platz and to tram 1 and 4 with a 10 minute wait
– direct connection to AB or Sprachzentrum

Busses

Bus 987: Neuberesinchen <-> Spitzkrug Nord
– leaves Neuberesinchen at ’29 (09:00 – 12:00), at ’13, ’43 (13:00), at ’43 (14:00 – 16:00) and does not run during the weekends, holidays (except 3 times on saturdays)
– goes via Neuberesinchen Bahnhof, Birkenallee, Südring, Westkreuz, Josef-Gesing-Str. and ends at Spitzkrug.
– direct connection to Birkenallee
– direct connection to AB and a good connection to Sprachzentrum
– direct connection to Kaufland

Bus 983: Bahnhof <- (Slubice) -> Bahnhof
– leaves Zentrum at ’45 or ’50 mostly all time (once in an hour)
– direct connection via tram 2, 1, 4 (but bad connection when going back (except tram 2), due to boarder controls and delays through traffic)
– connection to Slubice (Collegium Polonicum, Intermarché, Plac Frankfurcki)
– connection to European New School, co-working space, Biedronkà

N1: Covers the north half of the city (AB, Spitzkrug)
N2: Covers the south half of the city (Südring, Birkenallee, Mühlenweg)

And also:

Any tram showing Betriebshof SVF:
– these trams are going to Betriebshof SVF for parking
– you can take these trams
– you can always take this tram for going to Mühlenweg, just get down at the last stop and then walk the rest.
– It does not matter which number it says on it, it will take the same route like Tram one (from wherever it starts) and go to Betriebshof SVF.

Please note, that the timings listed are only for general orientation.
The timings change (especially for Tram 3 and 5) depending on the daytime.
As example, tram 5 and 3 have a gap somewhere around noon and only run for a short wile.
And the other trams (1, 2 and 4) accept a sunday-like schedule during the late evening.
Also, during the daytime tram 1, 2 and 4 run simaliar to the normal schedule on saturdays.
Please always check if the tram is actually coming or not.

Also, Tram 1, 2 and 4 are the primary trams, while 3 and 5 are just additional trams that only run during the school time and during the daytime. They are intended to stabilize the network more and to have more capacity for students.

You can check out the website of SVF to get more details on the schedules, there are also printable PDFs.
Here are the schedules for a few stations:
– Neuberesinchen
– Zentrum
– Dresdener Platz
– Europa-Universität
– Westkreuz
– Magistrale
– Witzlebenstraße

I’d also recommend you to take a look at this page, which shows the public transport network in a diagram.