Sentence Structure for past tense If I want to say 

"we were in(at) the shop on Saturday" 

would the translation be 

星期六我们在了店。(xingqiliu wo men zai le dian) ?

Same for this past tense,

If I want to say, 

"we were happy"

would the translation be 

"wo men shi le kuaile" ? because 'we were' would use the verb to be "shi"“是” and that would be in the past tense, add 'le'  '了‘?
This is one of the core conceptual mistakes that learners of Chinese make.
Let me try to shed some light on it:

了 does NOT express past tense, it expresses change. 

Why not past tense?! 


Because as 倪阔乐 has also stated, (1) there are no tenses in Chinese. 
And because (2) 了 can express change in the past, present and future, too. 


Let's just examine these two statements. The first one should not be that hard to realize, because in Chinese you do not conjugate verbs, in fact there is no such thing as conjugation in Chinese, so there is no exact corresponding term to express: 'was', 'wrote', 'had', etc. In Chinese, you express actions that took place in the past in a different way, most notably by adding temporal markers, like 昨天 (yesterday), 以前 (before, in the past), 当时 (in those times), etc. 了 may or may not be used in these sentences, it's entirely possible to construct sentences that recount past actions without using 了, e.g. 

我年轻的时候家里没有电脑。 When I was young, we had (lit. there was) no computer at home.

If I said: 我年轻的时候家里没有电脑了。, that would be different. The latter expresses the idea that in the past we had a computer, but when I was young my family somehow lost or got deprived of that computer (i.e. there was a change from the "state" of having a computer at home to the "state" of not having one anymore).

Also, to further illustrate that 了 and the past tense do not go hand-in-hand, let's take a look at this sentence:

哦，啤酒就很快没了！ Oh, we'll soon run out of beer!

As you see, here we express something that is going to happen in the (near) future, yet still use 了 – to express the expected change of going from the situation of having beer to the situation of having no more beer. And to have an example where 了 can be used to refer to the present, regard the following example: You sit at your desk at your company and your colleagues are Chinese, at noon one of them will shout: 吃饭了！ Time to eat! So why do we use 了? Because it express the change of interrupting your work and taking a lunch break. 

By now, I think, it should be clear that 了 and past tense are not connected. You use 了 when you want to express that there was, is or will be some change that you want to point out, regardless of the perceived tense (past, present, future) of the action or event. 

We can now go back to your examples and work them out:

We were in(at) the shop on Saturday There is not really a change here, so suppose you are telling your friend what you did on Saturday: 星期六我们在商店。 However, this sentence may also express that Saturdays you are usually at the shop. So, you may want to add some extra elements to make it clear, like last Saturday: 上个星期六. The context (previous sentences or earlier information about your usual Saturday activities) may also help the listener to understand what you mean.

The proposed translation of the other sentence We were happy. has two major mistakes. First, 快乐 takes the place of the predicate by itself, there is no need for 是 (as a copula, unlike the English is) [This is something you need to lookup in your textbook, I won't go into it]. The other mistake is the use of 了. As you by now know that it does not express past tense per se, it's just not going to turn your sentence into past tense. You have to express past with some modifier, e.g., by introducing something that expresses the temporal aspect. You could use 当时 or 那天, or many other words entirely depending on how and when things happened. 当时我们很快乐。 In those times we were happy or 那天我们很快乐。 That day we were happy. What the that day refers to depends on the rest of your story, when you say something like We were happy., you probably have already established the time frame in an earlier sentence, so it should be clear, or choose another  more adequate temporal marker.

So this is quite a bit of an explanation, and do expect some people to add comments on it, so please also check those, and most importantly consult your textbook or teacher on this for more example and exercises.