If you want to state what you think you can put と思います at the end of a sentence. However I noticed that sometimes you're supposed to put だ before と思います so that it becomes だと思います, and sometimes you're not. How do you know when to put だ before と思います and when to leave it out?
The と (to) of と思います works like the quotes in English. So the part before と must be a valid sentence.
○ 美しい と思います
× 美しい だ と思います (美しいだ is not a valid sentence)
○ 美しいんだ と思います (very strong feeling)
○ キレイだ と思います
○ キレイ と思います
Don't think of the だ as a part of it. 「だと思う」 is just 「と思う」 stuck to the end of a sentence that happened to end in だ.
The only time you might need to add an extra だ is if you use it as a colloquial-ish stand-alone reply in the same way as 「だね。」 and whatnot.
From Tae Kim's Guide To Japanese @ http://www.guidetojapanese.org/learn/complete/verb_phrase :
A verb clause can be phrased by adding 「と」 to the end of the clause. For verb clauses that end in an plain noun or na-adjective, we must add 「だ」.
So 「だ」 needs to be added before 「と思う」 if the last word in the clause we want to quote is a noun or na-adjective. Some examples of mine:
I'll be fine in the exam, I think.
Teacher's daughter is pretty, I think.
The person that made a mistake is the other party, I think.
If the last word is a verb or an adjective, you skip the 「だ」:
I thought it is a bit expensive so I did not buy it.
It is a bit expensive but I think I am going to buy it anyway.
There is one condition where you also skip the 「だ」 before a quotative 「と」, that is if you are quoting a name or a term, for example:
I am called Lukman.
That person is being called "Red Devil" around this area.
Each time you can write のです then you can write のだ.
Then you can combine this (using と) with a variety of verbs including: 思う、信じる、言える。。。
Here is what should be your thinking process when building a sentence:
"This is not correct." (less formal, more blunt):
"This is not correct.":
正しくないです。 (tadashikunai desu)
"I think this is not correct.":
正しくないと思います。 (tadashikunai to omoimasu)
"This is not correct." (attenuating with の):
正しくないのです。 (tadashikunai no desu)
"I think this is not correct." (with の, the sentence you're asking about):
正しくないのだと思います。(tadashikunai no da to omoimasu)
"I think this is not correct." (spoken form):
正しくないんだと思います。(tadashikunai n da to omoimasu)
As a short explanation, I wrote の = attenuation but this is not completely true. Depending on the context it can be used to emphasize the action that appears before の, to make your point...etc. Most of the time it is used in sentences like:
You can also use だと思います if there is a noun or anything that is not a verb before.
きれい is a な-Adjective and not a い-Adjective.
Therefore, it should be: きれいだと思います。
な-Adjective+ だ と思います
日本語の勉強は大変だと思います。 I think Japanese study is tough.
日本語の勉強はおもしろいと思います。 I think Japanese study is interesting.
Noun+ だ と思います
あの人はセンターの学生だと思います。 I think that person is a student at the centre.