That's kind of a tricky question, I guess. There are plenty of expressions in English that can't directly be translated to Japanese; our ways to converse with others are different. To me, "I hope" sounds like one of them. You can kind of substitute "〜たらいいんだけど (casual)" for "I hope". For example: I hope I explained well. → ちゃんと(うまく・わかりやすく)せつめいできていたらいいんだけど。 I hope I pass the test. → テストにうかればいいんだけど。 I hope I can go. → いけたらいいんだけど。 You can change the very last particle "んだけど" to "なあ(sounds a little strange in the first one)". Also, if you change the last part "だけど" to "ですけど or のですが(less common)", it sounds little more formal. However, I personally wouldn't use these expressions in speaking so often. I would probably rephrase in a different way. For example: I hope I explained well → もっとうまくせつめいできたらいいんだけど (I wish I could explain better.) → I might just ask if he or she understood my explanation. These are just my personal opinion. I hope it helps. Try to ask somebody else to see how they speak. How you express those things really depends on your personality.

As Yoshinori-san explained, "to hope" can be translated into many ways: I hope I pass the test. #1　テストに　うかると　いいんだけど（なあ）／いいんですが／いいのですが。 #2　テストに　うかると　いいな。 #3　テストに　うかると　いい(な)と　おもいます。 These three sentences are very similar, but are bit different. #1 has a connotation that I hope to pass, but I feel that I might fail. So, there are a bit negative feelings. #2 have positive feelings. #3 is a a bit polite version of #2. Also, there could be other translations for "to help", such as "きたいする" or "ねがう". #4 テストに　うかることを　きたいしています。 #5 テストに　うかることを　ねがっています。 #4 is a little formal and positive. きたいする is more like "to expect" , so the possibility to be realized is high. ねがうis more like "to wish", so the possibility to be realized is low. And, #5 is formal and is written word.