У нас были собаки. У вас будут журналы. Please note that "быть" must match the gender (for past tense) and singularity or plurality of the noun coming after it.

Past tense: У меня был - for masculine - У меня был журнал. У меня была - for femenine - У меня была собака. У меня были - for plural nouns (except neutral form) - У меня были журналы/собаки. У меня было - for neutral - У меня было настроение. Future tense: У меня будут - for plural - собаки/журналы. У меня будет - for all singular forms - журнал, собака, настроение.

Nope, neuter is used with quantities ("У нас было две собаки/будет много журналов") or non-nouns ("Завтра будет холодно") For normal plurals it is plural. Of course, as you become better at Russian, you'll encounter ambiguous cases dealing with "groups" that can be viewed as a whole or as a number of individuals. Gramota.ru has a good article on the topic — you'll be able to use it then. One such "advanced" example is something like "The majority of students were Americans"="Большинство студентов были американцами" (as you can see, it would not make sense to use singular "американец" here, so the verb follows, though, here it is just a recommendation). Basically, some advice dealing with such structure centers around how easy it would be to parse the sentence for a reader, and how logical it sounds.