Printing is so frustrating! ... HELP

[LMP87]

I try to print out 8x10s after my photo sessions, but I can't find the right resolution to print out! >_<
SO FRUSTRATING!
I can't seem to understand resolution on how to print them to come out right.. any info would help!

 

[KmH]

There is image resolution - 3862 x 2835 px
There is print resolution - usually somewhere between 100 ppi and 360 ppi.
Image resolution and print resolution determine print size.

And there is image and print aspect ratio - the rectangular shape of the print or original photo.
Most DSLR cameras make photos that have a 3:2 aspect ratio, which would make an 8x12 print (4x6, 6x9, 10x15, 16x24, 20x30 etc.)

8x10 is a closer to square (less rectangular) 5:4 aspect ratio (4x5, 12x20, etc).

To make a 5:4 print from a 3:2 photo requires cropping some from the long side of the 3:2 to make it closer to being square (1:1 aspect ratio).

You need to know 3 basic math equations:
pixels / ppi = inches
ppi x inches = pixels
pixels / inches = ppi

Your profile shows you have a Nikon D3100. The D3100 makes 3:2 aspect ratio photos that at the default setting have image resolution of 4608 x 3072 pixels (page 195 of your D3100 Reference Manual - Specifications = Image Size (pixels)).

So using the short side since it doesn't need to be cropped we use the last equation and calculate - 3072 px / 8 inches = 384 ppi.
With that we can then use the second equation to calculate how many pixels we need on the long side of the original - 384 ppi x 10 inches = 3840 pixels.
Now we can just subtract to calculate how many pixels need to cropped away - 4608 px - 3840 px = 768 pixels.

Print resolution of more than 340 ppi or so is pretty much wasted because human eyes cannot see an improvement in image quality above that.

Depending on image content and what editing has been done to the original, many prints look just fine at as low as 100 ppi.
We do have to take viewer distance into account and as print size increases so does viewer distance.

Printing is rather involved and there are color management and other technical considerations that also have to be accounted for like the type of print that will be made, be it a C-print or an inkjet print.
Tutorials on Color Management & Printing

The Digital Negative: Raw Image Processing in Lightroom, Camera Raw, and Photoshop

The Digital Print: Preparing Images in Lightroom and Photoshop for Printing

Fine Art Printing for Photographers: Exhibition Quality Prints with Inkjet Printers