How do I check the dpi for photoshop?

To add to D Fosse’s reply, optimise your images in Photoshop (in RGB color mode) and Place them into an InDesign document (ensure the Effective PPI of the images in InDesign is around 50 PPI for this size poster). In this document you can also indicate bleed, add background colours, text etc and (usually) export the document as a PDF/-4 for your printer - though check with your printer which type file they prefer.

Rule of thumb: For photographic content, any high quality file from a good current DSLR will work at any size. Magazine spread, wall-sized banner, doesn't matter. The bigger the print, the lower the ppi can be, because it will be seen from farther away.

If your file ends up in excess of, say, 12 000 pixels long side, you should think long and hard about whether that's really necessary. Usually it isn't.

If you have text and graphical elements, don't do it in Photoshop! Do it in InDesign.

Go by your printer's guidelines. One example:

Raster Files: For banners and signs designed to be viewed at less than 24", your resolution should be 300 dpi at final size. For designs that are to be viewed beyond 24", we recommend a resolution of 150 dpi at final size. For very large banners, signs, and displays that are going to be viewed from a distance, 100 dpi resolution is perfectly fine and will make it easier to work with the files.

https://www.northcoastbanners.com/digitally-printed-banner-art-requirements for complete information.

The standard reply is that this is acutally PPI not DPI and that you should not need a 300ppi file at 4x10 foot (1.45G RGB or 1.93G CMYK file)! It is all about image content, viewing distance, print method and other variables. Photoshop is probably not the best place to create such a banner in the first place, although elements of the banner could be created there, the layout should probably be done in Illustrator or InDesign.

To check the dpi go to the Image menu, choose Image Size make sure the Resolution is pixels/inch and that the number is 300.