I’m currently finishing up Latin and going to start reading the Wheelock Reader, but I want to start Ancient Greek because I want to study something similar to Latin. I’ve tried numerous books, though I do think I will use Mastronade’s Attic Greek along with Athenaze. I’m having trouble with accents, I just can’t grasp the concept and placement of these marks. Is anyone able to help? 
What exactly in Mastronarde cant you follow?
You are not expected to master accentuation completely at the first or even tenth reading. Mastronarde says in his instructions for working on the accentuations chapter:
“1. Read this unit carefully more than once. Return to review it every now and then during the course. (Further aids to accentuation will be given in later units.)”
It makes more sense to work through the chapter and ask specific questions here, rather than make a general request for an alternative explanation.
Mastronarde also says:
“The beginner should not be worried if the rules for accentuation given here seem complicated and difficult to master. It takes time and practical application before a beginner starts to feel comfortable with accents; but it does not help to ignore them entirely at the beginning and try to repair the omission at a later stage. In learning accents, there should be a happy medium between insouciance and an obsession that detracts from the learning of other elements of the language.”
Sage advice.
The most recommendable books on Greek accentuation are the two books of Philomen Probert, A New Short Guide to the Accentuation of Ancient Greek (2003) and Ancient Greek Accentuation (2006). The aforementioned is more concise and should be read first.
I don’t know what exactly are your problems, but offhand you shouldn’t feel too despondent—it may take a while to grasp the concept. At least it took me a while. But I can tell from experience that once it starts clicking, it may happen that you can’t get enough of accents.
Just a few quick remarks. You probably know already about the three different accent marks and that accent can be on one of the three last syllables in a word (with enclitic words there can be two), not further towards the beginning of a word. Acute marks high pitch on the last mora of the syllable, circumflex rising-and-then-falling pitch on a syllable; thus circumflex can be found only on long-vowel syllables (including diphthongs of course).
The limitation that only one mora can follow the falling pitch coming after rising pitch leads to that on the one hand only acute can be on the antepenult and only when the ultima has only one mora, and on the other hand that with an ultima with two morae circumflex cannot be on the penult, only on the ultima. Acute on ultima becomes grave if the sentence continues without a pause (marked with comma or the [semi]colon · in writing) and there is no enclitic leaning onto the word. Famous rule is the σωτῆρα rule: when accent is on penult with long vowel (or diphthong) and ultima has only one mora, Attic will always have circumflex.
Verbs are recessive, i.e. they have accents as far from the end as possible (preverb limitation! when monosyllabic verbforms have a prefix, the accent cannot move on the first syllable of the prefix), except for some infinitives and participles. Vowel contraction often makes a circumflex (if the accent is not on penult ultima being two morae), but not in words like ἑσταώς > ἑστώς with the original accent on ultima.
In other dialects there can be differences (our knowledge is, to be sure, limited on them). Famous will be the Lesbian barytonesis, i.e. accent will be as far from the end of the word as the last syllable permits. Thus we’ll have Σαπφώ in Attic but Ψάπφω in Lesbian.
With nouns much has be committed to memory (there are guiding, helping patterns, check Probert 2003). Generally the nominative accent is preserved through the inflection (if the last syllable permits). There are many interesting details here, but I’m not sure we should go to them at the moment.
The most recommendable books on Greek accentuation are the two books of Philomen Probert, A New Short Guide to the Accentuation of Ancient Greek (2003) and Ancient Greek Accentuation (2006). The aforementioned is more concise and should be read first.
These are excellent books but are emphatically not suitable for beginners.
As Probert says in the preface to her short guide " This book is also not an introduction to the principles of Greek accentuation for those embarking on the learning of Greek who are in the happy position of learning the accents of individual words while learning the words for the first time. This method is really the best way to learn Greek accents, and for this purpose there are several grammar books with good sections devoted to accents; one might also use KOSTER’S A Practical Guide for the Writing of the Greek Accents"
Her Book, she says “is for those who already have some knowledge of Greek, but either no knowledge or shaky knowledge of the accents”.
I suspect the difficulties lie in the use of terminology such as mora and enclitic etc. As I suggested perhaps the original poster can tell us what the specific problem is.
As Timothée says there is no need to be despondent and many people here have only a shaky grasp on accentuation. I first learnt Greek from someone who didnt understand or use them at all. In the large scheme of things its only a (small) part in learning Greek.
Although the layout is very user-friendly, the exercises in Koster look (to me, at least) like they would be pretty difficult for a complete beginner.
As I mentioned in another thread, Mastronarde gives you all the information you need to understand accentuation at the start of the book. That information didn’t make a lot of sense to me the first time (or even the first five or six times) I read it, though. It looks, and is, confusing at first. As you work through the first three or four chapters, get into the habit of flipping back to the beginning of the book and finding the specific rule that applies to that particular case each time you don’t understand why a certain accent occurs where it does or changes for no apparent reason. If you keep doing this, you’ll eventually learn to apply the rules instinctively, but it takes time.
And as Seneca said, if something specific is confusing you, ask about it here. 
It might be helpful to learn the main rules (not every last detail) by rote from a list (which should be easy to find on the internet) and once they’re absorbed to return to the chapter in Mastronarde. I did it that way (knowing the rules from earlier attempts at learning) and there was just a sense of “oh, so that’s how it works.” Athenaze does it piecemeal as well.
This may be horrible advice though.
I want to thank everyone for such great advice!! I’m finding my way through learning these marks! I just finished up Latin, which allows me to give more attention to Greek!!