I'm afraid, you do have to memorize all those forms of all the nouns (and the adjectives too

), at least at first. Hopefully later you start recognizing patterns and it gets easier. Although since there are so many exceptions in Estonian, it may not get very easy.
In case of foreign and (more recent) loan words, it should be usually quite straightforward:
If it ends with a vowel, then nominative and genitive forms are usually the same and "
-t" or "
-d" (in case of double vowel) is added for partitive;
If it ends with a consonant, then usually "-i" is added for the genitive and "
-it" or "
-i" (if the last syllable is stressed and can be made overlong) for partitive;
But of course there probably are exceptions.
Linguoboy is right. If you hear all those forms all the time, it takes no effort to memorize them. These forms are not something that are additional parts to a word -- all those forms form a word -- it's like declenation is an additional dimension in which a word exists.
But I too have felt uncertain about some words that I have rarely or never heard before, then I just look them up from the
ÕS.
PS: I have noticed that foreigners have sometimes trouble with plural partitive too, because some words also have short plural partitive forms in addition to more regular suffixes. In some cases those short forms are preferred over the long ones. The same goes for illative case too.