I'm new to After Effects and Adobe Products in general. I'm currently using a free typography template.
The template has 8 compositions and I'm trying to arrange the compositions to play in the order I'd like them to play.
I tried copying/pasting the layers into a pre-existing composition but the text overlaps with the other text layers.
I also tried to pre compose the layers and then copy/paste that into a composition but it also overlaps. Then I tried to drag it to the bottom and/or move the bar on the sequence but it won't appear when i play.
Any help would be great!
I am not sure I understand what you're asking for.
When you say it "overlaps", what do you mean? Do you mean that they're over the top of each other and you want them to play simultaneously, but spaced out better? If so, change the position and scale of your precomps.
If you're just trying to get them to play in order, select them all and Animation>keyframe assistant>sequence layers.
Unless I completely misunderstood your problem, this is very basic stuff in AE. I highly recommend that you start here.