Whats the best way to accomplish this? I can handle pretty simple rhythms, but I seem to have issues with dotted notes, eighth notes when they are by themselves, and triplets. What are the best ways to get used to these things? Should I just count them out? It feels even more difficult when I try to over thing these things. Any tips?
Practice at a slow tempo and gradually work your way to faster tempos. If you know what the rhythms are - and I have no reason to think otherwise - you'll be able to play the riff at a slow tempo.
Double it - play it slow and double the length of all the notes in your head, so 16th notes become 8th notes, 8th notes become quarter notes. That way a single 8th note becomes a simple quarter beat, a dotted quarter note becomes 3 quarter beats (ie a dotted minim)

Work out ways of counting different lengths of note too - for example if its mainly 8th notes you can count it 1 & 2 & 3 & 4 &, if its mainly 16th notes it becomes 1 e & a 2 e & a 3 e & a 4 e & a, triplets can be tri-pl-et.

So if you've got a quarter note followed by a quarter note, 4x16th notes and 2x8th notes you could count it: tri-pl-et 2 3 e & a 4 & ....against something holding the beat for you. If you've got a metronome set it so you can keep the main quarter beats on the metronome click.

I dunno if that made much sense, but if it did it should help.

Edit: work out the rhythm before you try and play it too - try tapping it out, then strum it on muted strings, then put the right notes back in.
Listen to the drums, get the rhythm in you head. If you need to actually read the music, find out what the rhythm sounds like and play off of it. If you can't do that: Counting is broken down into parts, and then into equal parts in relation to the previous note.
Imagine a pizza. The initial way you cut it is your time sig. How you cut it the second time is your pulse. How you cut each piece is the differentials in each note. Rests are eaten pieces. (Rests are very important).

If you need to see it, take a drum class on reading rhythms. Learning how to play the drums can only help your musical ability. Dancing can do the same thing.
I am the only sane person on the planet. Does that make me crazy?

Crank the Mids