It's relatively a long time that I use English on a daily basis and I feel pretty comfortable with the language but yet there is an issue.

I have doubts concerning articles ''a'' / ''the'' even though I know the rules of grammar.

Especially it is difficult to figure out in a case when I have a doubt whether there should be *the article or there is no article at all.

For example: last year / the last year, previous time / the previous time, etc

How do you, native speakers feel with regard to using that ??

Hmm...difficult! Here's what comes to mind:

"last year" = the previous calendar year
= I went to China last year (=2014).

"the last year" = either "the final year (of something)" or "over the last year" (=over the past 365 days)
= The last year of school (=final year) is the most important.
= We've lost nearly half our social referral traffic in the last year (=from November 2014-now).

"the previous time" = correct

I can't think of a situation off-hand when I would say "previous time" by itself unless I was just omitting "the" to save space (say, on Twitter or in an instructional manual, where precise grammar is not so important). I might say "my previous time (doing something)" or "at a previous time," but not "previous time" with nothing before it.