I have some cells that just have plain integer values and would like a way to add 1 to them all without having to manually do it in each cell. Sorry if this is really simple; I have little to no experience with spreadsheets.
Excel has a special paste option which lets you add a number, say 1, to all cells in the selected range. Sadly, Google Sheets doesn't have it: Where is Excel's Paste Special Operations in Google Sheets?
That means you'll have to perform multiple steps, with some temporary cells, to do this:
Create a cell with a formula like this one:
Use the autofill function, by double clicking the little square in the right corner or by dragging it down. Select all newly created cells:
Select the original cells, and choose 'Paste values only' from the Edit → Paste special menu:
That increases the values of the cells by one. You can now remove the temporary cells.