What are some ways I can learn Chinese characters effectively?
I'll assume that you want to learn vocabulary (written character form, pinyin pronunciation, and translated meaning).

I'll start off with a little about how I learned (just passed HSK 3 after 9 months of study from zero background). First I completed some smartphone apps (ChineseSkill, Hello Chinese, and Chinese InFlow), then I studied the review and flashcards provided with those apps. I then progressed to composing my own sentences usually using Google Translate along with Pleco dictionary. Then I started using Anki flashcards. I also made my own Excel spreadsheets for random quizzes and handwriting templates.

Here are some tips that have helped me:

1) In the initial stages go slow and try to learn a few characters and basic sentences like 我是男人。

2) Try to figure out tricks to help you remember the characters. For me 是 looks like the word "BE", so I instantly memorized it with no problems. I learned 我 by thinking of the saying "woe is me". I learned 写 by thinking it looks like the letter "E" for french "écrire" I always thought in my head "écrivez". I also invent my own little names for the characters/radicals 京 is "beijing man" because it looks like a little guy with a hat and mustache. 听 at first looked to me like a person hitting a hammer on an anvil or someone hitting a tuning fork, so it was natural for "hear/listen". 近 looked like a person trying to avoid a cat with it's tail raised (who like's seeing a cat's but, really?!?!!? ;) "too close for comfort", so it means "near". Of course, some of this is inconsistent and silly, but it was a fun way to remember things.

3) Also learning the decomposed radicals can be helpful. 要 is "western women" who are indoctrinated into materialistic culture and always "want" things. Some of this is meant to be funny, but it has worked for me. 好 is "woman and child is good" as in a woman who gives you a son is a good thing (yes, very sexist, but it is what it is and helps to remember). Sometimes I just remember the radicals like 照 is sun+knife+box+heat which I think of as taking a photo and cutting the film and developing it in a "hot" chemical solvent. I know the "box" is really mouth, but "box" is quicker for me to remember. Invent your own little mnemonics. Of course, ultimately it might be wise to learn the actual true radicals and their meanings, but initially I think anything that helps you remember is good.

4) Learn at least a few characters by handwriting with the correct stroke order. I think this is what really pushed me over the edge in terms of my understanding of the characters, what they mean, and why they are composed the way they are. I can write all 600 HSK 3 words by hand, and probably 100 other words. Make sure to get the stroke order correct!

5) Practice writing your own sentences, I use google translate and the standard android pinyin keyboard. It will help you recall the vocabulary better.

6) I have neglected tones and speaking, so I am bad at that. I can understand listening pretty well. But I am also a musician, so learning and remembering the tones is sort of easy if I try, but I have just neglected it. You would probably be advised well to concentrate on learning the tones as you go along and not do what I have done by neglecting them. I have perfect tone identification by hearing, probably due to my musical training.

7) I have also neglected grammar. However, I can quickly read HSK sentences and know what they mean just by seeing the vocabulary involved.

8) Use Pleco, Anki, or other flashcard systems.
      - show character and test your recall of the pinyin and meaning
      - show pinyin and meaning, test your writing the character
      - play sound and test your recall of pinyin, character, and meaning.
   Do at least 100 flashcards a day for a year. Don't cheat yourself, 
   make sure you are honestly recalling things.

9) Practice speaking (I use Google Translate, Pleco, and ChineseSkill/HelloChinese). I speak a sentence or word into the app until it understands it. That helps to practices getting the tones correct.

10) Use MDGB for other flashcards/quizzes/dictionary. Look up character stroke/radical decompositions. You don't have to memorize these, but they are helpful with gaining an overall understanding of the language.

Once you build up a few hundred words of vocabulary it continually gets easier learning new words as they use many of the same characters, strokes, and radicals. It becomes easier to guess rough meanings and pronunciations. Grammar is more difficult as there are some many specific grammatical forms, but getting down the basics of grammar in terms of sentence/phrase order will enable you to compose sentences that a native speaker can understand even if not totally correct. Use AlleSetLearning website for awesome grammar lessons.

Sorry for such a long post, but these are some things that helped me starting from scratch. Hope you find it helpful.