Translation:I think Ms. Tanaka will come to the party.
田中さんは自分がパーティーに行くと思っています。 Jibun=oneself. The verb changes from coming to going depending upon who will be doing the coming/going. If you ask someone: "Are you coming?", they will respond: "yes, I'm going". Also, when speaking about a third party, you usually don't use omoimasu, but omotteimasu or omottemasu (shortened form). Example: Mr. Tanaka, what do you think? 田中さんはどう思いますか？What does Mr. Honda think? 本田さんはどう思っていますか？
Some people (possibly a lot of people) might omit the titles even with a last name in English. It really depends on the custom in your area. I do know that Japanese use last names far more often than is common now in my area. However, I do think we should translate last name + san to title + last name in English.
How do I know whether I or Mr. Tanaka is the one who thinks? What stops this from being "Mr. Tanaka thinks of coming to the party"? Is it that 考える performs the functions of "thinking about"? According to jisho.com, 思う could also mean "to plan on" or "think of (doing)" which is why I ask.
はず is a word that can be tagged onto the end of a verb to give the sense that something is expected. In this case, 田中さんはパーティーに来るはずです。 Would say "I think Tanaka is coming to the party (Because they just texted me, or they told me earlier today, et cetera.)" Just a bit more specific way to say this, as 思う feels more like an opinion than expressing information :)
There is no future tense in Japanese. You would say basically: "tomorrow, I go to party". As long as the sense is indicated specifically with tomorrow, next week, etc. it is clear. 明日学校に行きたくない (Ashita gakkou ni ikitakunai) I don't wanna go to school tomorrow. 来年大学に入ります (Rainen daigaku ni hairimasu) Next year [I, he, she, it] [enter, enters] university. Please keep in mind that these are definite statements. If it is conjecture or something which is likely but unknowable a qualifier must be used (なるでしょう＝will likely become). Don't fret too much on this one yet, though.