It's all in the topic. I don't have the best guitar around, but what would be the best way to fix it? Should I take it to someone or can I do this myself?
Action is always higher at the higher frets, but you could try adjusting your saddles.
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I got the same problem, the action was too high at my higher frets. I lowered my saddles and now it's Too low at the lower frets and yet, it's Too high at the higher frets.
What's with all the plural of "saddle" in here? An acoustic guitar has but 1 saddle, it's the white piece fit into the slot in the bridge.

TS, it's normal and necessary for the strings to be farther from the frets at the body end of the neck versus the headstock end. This allows for you to fret the strings without them touching the next fret. Imagine if the strings were all parallel to the frets, when you pressed any of them down to play the guitar, there wouldn't be room for it to vibrate because it would be too close, making the guitar basically unplayable.
Action is adjustable on an acoustic but should be done by someone in the know. You can do it yourself, but not like others above have stated(I'm thinking they're all electric players who're in the wrong forum). To lower action on an acoustic you need to remove the saddle piece and sand down the bottom of it a little, then place it back in and re-tune to see where the action is at, then repeat as needed. If it's too low at the headstock end, then the nut would need to be removed and replaced with a taller one, though personally I enjoy having the action at that end as absolutely low as it will go without any buzzing on open strings. It makes for much easier barre chords and fretting of the open chords/notes at the 1st, 2nd and 3rd fret positions.
If completely unsure or just want a second opinion, take it to a guitar tech and have it examined. It shouldn't cost for an estimate for repairs, if any are needed.