Understanding the difference between sheet formats and drawing templates confuses many new users. I know it took me a while to get straight. Sheet formats (slddrt files) and drawing templates (.drwdot files) are two completely different file types. Sheet formats control sheet size, sheet orientation (landscape or portrait), border lines, table anchor points, and title block notes. These title block notes are typically driven by model properties or Drawing properties, which can be accessed by going to File > Properties in the Drawing. You can edit a sheet format by clicking on a blank part of the sheet, the sheet tab, or the sheet name in the tree, and choosing "Edit sheet format" from the drop-down. (By the way, any existing drawing views and annotations that don't belong to the sheet format will disappear when you go into "Edit sheet format" mode. Don't worry. They'll come back.)
When you're finished with your edits you can click on the icon in the upper right corner...
...or right-click again and choose "Edit sheet" from the drop-down to exit the sheet format editing function and return to normal operation.
You can save your sheet format by going to File and selecting "Save sheet format" from the drop-down.
You can change to a different sheet format by expanding the Scale drop-down in the status bar at the bottom right corner of your monitor and choosing "Sheet Properties..." (This drop-down hasn't always been available, so if you're using an older version you can right-click again to get the same menu shown in the first screenshot above, but this time choose “Properties…” instead of "Edit sheet format".)
This will take you to the Sheet Properties dialog box (screenshot below), where you can set the sheet scale, change or Reload the sheet format, name the sheet, etc. When inserting a new sheet, it will use the same sheet format as the active sheet by default. (If you don't want it to use the same as the active sheet and instead want to choose the sheet format when adding sheets, go to Tools > Options > System Options > Drawings and check the box for “Show sheet format dialog when adding new sheet”.) If you don't see your saved sheet format listed here, and it's saved at the location you're pointing to at Tools > Options > System Options > File Locations > Sheet Formats, then un-check the box below for "Only show standard format".
Speaking of switching to a different sheet format, starting with SW2017 we can change the format for multiple sheets with one operation. Choose the new sheet format, then click on the button shown below.
That will bring up the "Sheet Selection" box. The active sheet will be selected by default, but you can add sheets as needed, or select "Sheet" at the top to update all sheets.
By the way, you might have noticed above in the Sheet Properties dialog box that First or Third projection angle is set there. I've never understood why. I'd think that option should be at Tools > Options > Document Properties where it could be set in the drawing template.
Layers are saved in sheet formats, which I learned by accident. I had added some Layers to one Drawing that I only needed for that specific project, but after that I'd have them show up after I'd worked on a new Drawing for a while. I finally figured out that I had apparently edited and saved my sheet format after creating these Layers, so these Layers would show up when I'd add a new sheet. I deleted the Layers and re-saved the sheet format. That fixed it.
As I said above, the title block information is typically driven by custom properties, so if you're constantly opening the sheet format to edit notes I'd strongly suggest you spend some time learning more about custom properties. In my opinion it's one of the most powerful tools the software has to offer, and will save you a tremendous amount of time, especially if you have Drawings with multiple sheets, since you can enter or edit the information once and it will populate all sheets, and it will greatly reduce the chance of errors. You should only be editing the sheet format to modify other things, such as updating logos, company address, or just the general layout of the title block. I go months without touching mine. See the screenshot below. It's from a newly opened Drawing using my standard template. I enter the information in the Value / Text Expression column and the notes in the title block are automatically filled out for all sheets. In the "Sheet 1 of 1" note, both numerals are linked to properties and will update as sheets are added. The "Draw3" note in the bottom corner is linked to the file location and file name, and will fill in accordingly when the drawing is saved, and the "Scale" note is of course linked to the sheet scale. As I said above, while I don't, many people also have notes in their title blocks that are linked to properties in the model, and those will update when a drawing view is inserted.
If you aren't familiar with linking Notes to properties, it's as simple as clicking on the "Link to Property" icon in the Note property manager when the Note text box is active, selecting either "Current document" (for Drawing properties) or "Model found here" (for model properties), and then choosing the property from the drop-downs (see below). If you're trying to link to a model property and don't see the property in the drop-down then insert a drawing view for the note to reference. You can delete the drawing view later if you want. (You can link to a property without going to the "Link to Property" icon, in which case I don't believe you'd need a drawing view inserted, but to be honest I've never bothered learning the proper syntax to type in.)
Now for Drawing Templates. They contain a tremendous number of settings that are controlled at Tools > Options > Document Properties, and can contain a sheet format. Printer settings are also saved in the Drawing Template, so if you have a template that uses a portrait sheet format, but when printing it prints in landscape, open a new drawing with this template, change the printer settings to portrait, and save the drawing template. Drawing templates are saved by going to “File > Save as” and selecting "Drawing Template" from the drop-down for file type.
If your drawing template contains a sheet format, but you'd rather have the option to select a sheet format when starting a new drawing, open a new drawing using an existing template, right-click on the sheet format in the tree, and choose "Delete".
Save your drawing template as shown above. Now when starting a new drawing with this drawing template you'll be immediately prompted to choose a sheet format. Of course the reverse is also true. If your drawing template doesn't contain a sheet format and you want it to, you can open a new drawing, choose the appropriate sheet format, and save as drawing template.
Here's a part that throws a lot of people off. When you start a new drawing it will use the sheet format as it existed when the sheet was inserted in the drawing template, or when the sheet format was last edited and saved in the drawing template. The drawing template does not maintain a link to the sheet format file, so if the sheet format is edited in another document it will not automatically update in drawing templates. If you want your drawing template to reflect changes to a sheet format you can start a new drawing, go to Sheet Properties, and click on the Reload button to update the active sheet. (I've occasionally run into a situation where the Update button doesn't work. If that happens, change to another sheet format, click on the "Apply Changes" button, then go back and choose the original format. That's never failed to work for me.) If you have multiple sheets saved in your drawing template don't forget to do this for each sheet. Then re-save the drawing template. This is why the Layers I talked about above weren't there when I'd start a new Drawing, but would show up when I added sheets.
The information above about new drawings using sheet formats as they existed at the time the sheet was inserted is of course also true for existing drawings. If you open a drawing that contains a sheet format that has been edited, you will need to Reload the sheet format to update it to the latest saved version. As I said above, if your Drawing contains multiple sheets, and you're using SW2017 or later, you can update all sheets with one operation.
By the way, I strongly recommend saving all custom document templates, sheet formats, weldment profiles, etc. in a location other than the SolidWorks installation folder so you won't lose them when you upgrade to a new version. If you're a single user save them somewhere else on your hard drive (and it wouldn't hurt to back them up somewhere else). If you're in a multi-user environment they should probably be saved on a network so other users can access them, and to help maintain uniformity between users. Be sure to point to the proper location for each file type at Tools > Options > System Options > File Locations.
2019-06-19 edit: Added the part about using the icon to exit "Edit sheet format" function. Thank you Tom Gagnon (Edit sheet format, trapped with no close edit icon ).