If I say
I went to watch my team play football.
do I say
Ich bin gegangen, meine Mannschaft Fussball spielen ansehen.
or
Ich bin gegangen meine Mannschaft beim Fussballspiel ansehen.
If I say
I went to watch my team play football.
do I say
Ich bin gegangen, meine Mannschaft Fussball spielen ansehen.
or
Ich bin gegangen meine Mannschaft beim Fussballspiel ansehen.
This is an interesting question, as it clearly demonstrates the big advantage of English: its utter economy and briefness. It is difficult to express your sentence briefly in well-formed German without completely changing its syntax.
Well-formed variations of your sentence "I went to watch my team play football" in typical everday German would be:
Ich bin zum Spiel meiner Mannschaft gegangen.
Ich habe meiner Mannschaft beim Match zugeschaut.
Ich bin nach München gefahren, um beim Match meiner Mannschaft zuzukucken.
Ich bin zum Bundesliga-Finalspiel meiner Mannschaft gefahren.
Now, this does not really answer your question because - I suppose - you are rather interested in the possibilities of German syntax, not in situative appropriateness of expressions. So if you want to stick to your very sentence, you can use the following German sentence. It is well-formed (in terms of grammar etc.), but it would not be used in that form in normal communication.
Ich bin gegangen, meine Mannschaft spielen zu sehen.
A sentence like this sounds as if taken out of a novel from 1920 or so. Very honed style. You simply would not say this usually, especially not when speaking about football. Rather perhaps when speaking about opera:
Gestern sind wir in die Oper gegangen, um endlich mal die Callas singen zu hören.
Note that although "Ich bin gegangen xyz zu tun" is technically correct, it is unusual. Usually you would support the verb "gegangen" by information "where" (as in: "Wir sind in die Oper gegangen").
Back to your football team, you also could say:
Ich bin meine Mannschaft spielen sehen gegangen.
This is technically a correct German sentence, although practically a bit unusual, probably because the chain of verbs ("spielen sehen gegangen") causes discomfort to most users.
You can play with this syntactical model:
Gestern hätten wir den FC Bayern spielen kucken gehen sollen.
(Yesterday we should have gone see FC Bayern play.)
This again is correct grammar-wise, but still the syntax is so manieristic that one would say something like this rather for linguistic entertainment.
There is one more option: use grammatically incorrect (or stylistically problematic) phrases. E.g. I could imagine overhearing a dialogue like the following somewhere in the Munich underground:
A: Hey! Na wie geht's? Was machst du?
B: Ich fahr ins Stadion, Hannover 98 kucken.
A: Echt? Bist du ein Fan?
B: Nee, nicht wirklich. Aber ich hab mir vorgenommen, dieses Jahr jede Bundesligamannschaft einmal zu sehen. Gestern war ich Stuttgart kucken.
Note that large parts of the proper information are not expressed explicitely. B says "Ich fahr' Hannover 96 kucken". Hannover 98 is a football team. B does not say "Ich fahr Hannover 96 spielen kucken" because it is simply clear that what he is going to watch is them playing football. That's what a football team does. It is understood to be so self-explanatory that it is not mentioned explicitely. It would be different if the team was to do something out of the regular order:
Ich fahr in die Oper, die Mannschaft von Hannover 96 den Freischütz singen hören.
This is casual (oral, everyday) language. In more refined written German you would say:
Ich fahre in die Oper, um die Mannschaft von Hannover 96 den Freischütz singen zu hören.