We use the construction ohne … zu when we want to limit or negate something. 
Karsten geht nach Hause, ohne ein Wort zu sagen.
Karsten goes home without saying a word. 
Mike hat zwei Monate Urlaub gemacht, ohne viel Geld auszugeben.
Mike went on holiday for two months without spending a lot of money.
Ohne ... zu is an infinitive construction (Infinitivkonstruktion). Infinitive constructions are made with zu + infinitive. 
Even though the name might seem to imply that they are something complicated, they are really easy. 
We just have to bear two things in mind:
Let's look at an example:
Karsten ist einfach gegangen, ohne sich zu verabschieden.
Karsten simply left without saying goodbye.
Karsten left.  | +  | Karsten did not say goodbye.  | 
→ Subject in main clause  | =  | Subject in subordinate clause  | 
→...zu verabschieden  | →  | Infinitive with zu at the end of the sentence  | 
That's it! Easy as that :)
Don't forget: if a verb is separable, zu goes sandwiched between the prefix and the main part of the verb!
→ Mike hat zwei Monate Urlaub gemacht, ohne viel Geld auszugeben.