"im Krankenhaus" is the same as "in dem Krankenhaus" even though not in every case. If you say "in dem Krankenhaus" you wanna bring out in WHICH hospital someone or something is. Its a certain hospital. Also Dativ of the article "der". "im Krankenhaus" can mean that the one you talk to already knows which hospital is talked about. Or it can mean that you wanna bring out that your at this kind of place right now. "Ich bin im Kino" if some calls you during the film and you wanna end the call fast. In the case of the hospital "Er ist im Krankenhaus" it would mean that someone has to be treated there.Whereat "Er ist in dem Krankenhaus" would only mean that his position is in a certain hospital right now. That only works with male (der) and neutrum (das) genders.

Firstly, frag DEINEN Lehrer. You surely have to have all of the declination tables learned by heart or at least on a nice summary note, that's the basic thing. Search for 2 tables: bestimmte Artikel (der) and unbestimmte Artikel (ein). When the time comes, you'll also have to learn the declination of adjectives after bestimmte Artikel, unbestimmte Artikel and ohne Artikel. Now 'dein' follows the pattern of declination of unbestimmte Artikel (ein), that's why in Dativ it takes the form of 'deiner' (for die/eine) and 'deinem' (for der/ein). So that's for the declination, you have to be careful about the gender and do a lot of exercises. I only started to use it intuitively after 3 or 4 years so don't be frustrated, we all go through it :) Now the cases. Genitiv (wessen?) is hardly ever used, don't worry about it for now. It's important to differ the questions for which we use Dativ (wem?) and Akkusativ (wen?). French doesn't have cases so you should look for a good explanation in a grammar book. Generally wem? corresponds to 'to who?' (To who did you give the book?) and wen? to who? (Who did you see? Who did you touch?). I know it doesn't really make sense this way.