They are grammatically nothing wrong but we say neither of them in coversation. we usually omit subjects in informal conversation. Like if someone asked me 寒い？I would say 寒い。 私は寒いです。: ～は…です。It emphasizes　…. When you want to put stress on 寒い you can say 　　　　　　　　　　　私は寒いです。 私が寒いです。：～が…です。it emphasizes ～. When you want to put stress on 私 you can say 私が寒いです。For example, if you were with many people, one of them asked you all if you feel cold. only you felt cold, then you could say 私が寒いです。 makes sense? If you don't understand let me know. I'll give another example.

Yeah I know Rosetta Stone although I have never used it. Its a software that you can learn Japanese or any languages like playing games, right? I feel like I used to know some good web sites for Japanese learner before. But I would recommend to read Japanese manga or commics for your conversational grammar since its been true that the expressions used in mangas are pretty much natural verbal Japanese. Then after practicing with mangas, you maybe able to start reading novels if you want. I would say reading mangas is one of the best way for JSL to learn natural Japanese unless your study aim is to take/pass Japanese examinations or sth..................................

To make the point extra clear: は marks the topic of the sentence. が marks the subject of the sentence and is often used with specific verbs, such as 分かります=To understand. (それが分からない, not ...は分からない） Because of this, the が would stress your 私 in your examples in a way you'd probably not desire. 私は寒いです。= I'm cold. 私が寒いです。= Its is me, not him, not her, but me, that is cold. (implication) Also, は can be translated as 'As concerning me, ...'. You're making yourself a topic. Imagine a situation where a teacher asks: 田中さんはどなたですか。= 'Who is Tanaka?' Here, 私が田中です would sound more natural than 私が田中です。 The first implies that I'M Tanaka, whilst the latter presents it like a random fact. If I were you, I'd use Minna no Nihongo. If you want something a bit more playful, then try learning from 'Let's Learn Japanese', which can be found on Youtube I believe. Good luck!

「～は」・・・「私は走（はし）りたい。」 「～が」・・・「私が走り（はし）りたい場所（ばしょ）。」 How Japanese decide how to use these words... It is what they want to say after these words.

Okay, I understand what you are getting at. I realize that my Japanese isn't natural just as with anyone learning a new language. I think the problem is that I am learning from Rosetta Stone (which has been pretty nice), but I feel like it won't instill natural tendencies. Is there another resource that will help me on this? Also, thank you all for the help on this subject. I guess I should have searched first before posting. (I'm new to italki). Again, thank you!