I must say, the last advice was the best. Radicals increase your kanji acquisition power, pure and simple. Because then you can relate similar kanji - kanji with the 'heart' (心) radical, for instance, usually denote emotions or mental states. 愛(love; kokoro is not the radical but it is part of the kanji)、恋(love)、情(emotion), 感(feeling, feel), 悩(troubles), 惑(annoyance), 惰(inertia, laziness), 怒(anger), 悲(sadness), 怠(laziness), 志(will, intention, aim, purpose)、想(thoughts, feelings)、思(think). Those are just the few I could think of off the top of my head. Or, if you know the radical for seashell (貝), which was used as money by the ancient Chinese, then you can know tons of characters related to money. 貨(currency), 貸(lend), 費(expense), 賃(wage, fee, rent, etc.), 買(buy), 資(capital), 貧(poor), 貢(tribute) just for example.
1) That's why radicals are important. Because your mind works by grouping similar things. And radicals can only make that grouping easier and faster. They will also have the effect of making those huge, scary looking kanji seem much easier because you will be able to break them down into their component parts.
Complex kanji are not necessarily more difficult than simple ones. It's a matter of how easy it is to differentiate the kanji from others, and how concrete a concept it represents. For instance, I once heard about this really young Japanese kid who knew the Kanji for monkey 猿 (saru) and he was only in first grade. 'Monkey' is just a very concrete concept so it was easy to remember, as opposed to say...解 which means 'solve; understand; melt.' The first two definitions at least are pretty broad concepts.
2) Write each new kanji 20 times. Take your time too - you want to write legibly, and believe it or not legible writing makes it easier for
you to remember the kanji.
3) Make sure you follow the stroke order diagrams or else you will never be able to write kanji in cursive (gyoushou).
4) Try to read the kanji in context. Either in a textbook or the genuine article - Japanese newspapers, magazines, websites, whatever. Don't be discouraged by huge amounts of kanji that you will find - just remember your purpose is to recognize only those kanji that you know. And you'll say, "Hey! I know that kanji! Awesome!" You can learn about total comprehension of the text later.
5) You also need to learn how kanji operate - that is, in what ways they combine. Certain kanji, for instance, act like the un-, in-/im-, non-, anti-, etc of English. 無、不、反. Those three are VERY useful. Learn about the types of kanji. The most common is a combination of one part that provides meaning and another that provides a sound. It's not always as clear cut as that, but for instance: 義、儀、議、犠. All four of those are pronounced 'gi,' which is provided by the first kanji in the list, and it has a meaning of...well, 'meaning.' There are many other such lists I could make but I think I got my point across.
6) And as the first replier said, USE FLASH CARDS! I have...4000 some flashcards, mostly of kanji compounds and some of kanji. I used flash cards when I was beginning and I'm using them again in my 7th year of study to help me remember the bigger and more esoteric compounds. For that purpose they are absolutely indispensable.
7) Many Kanji have multiple pronunciations and multiple meanings. Don't try to master all of them at once. 出、上、行、掛. Those are some very basic kanji that have multiple meanings and readings. It's best to learn the various readings and meanings as you go, acquiring more specific ones later. Learn 行く (iku, to go) first, then later you can learn 行う (okonau, to do, practice, conduct). Of course, it may be easier for you to learn both at once. I can't speak for all learners. You can decide how much you are capable of biting off at once.
8) Lastly, take your time! It's not easy acquiring kanji.
Even Japanese people take their entire pre-college school years learning them. If kanji are part of what attracted you to Japanese or you just think they look cool, that will probably make learning that much more fun. And that's good. You should treat it as fun or else you may just give up like so many I have seen.