I am trying to resize a tif or jpg file to submit somewhere but am confused. I am told my file must be at least 96dpi, at least 1920 pixels longest side but be under 3MB. When I resize my image to the minimum it is overt 7MB in size. Am I missing a trick here? Should I be somehow reducing the quality - if so how do I do that?
TIF's make large files, JPG is fine in most cases, such as for circulating the image to others and for use on websites.
For what purpose will your image be used for? If it's for a website the PPI (what you called DPI) is irrelevant.
What are you trying to resize it to – you can use Image > Image Size in Photoshop to reduce the dimensions and use Save As and the JPG Options to increase the JPG compression, selecting the amount depending on the acceptable quality of the compressed image.
The question to you what file format are you saving. You should be saving a flat images like a Jpeg imags with a high quality setting 10, 11 or 12, You want to submit a high quality image that has a large number of high quality pixels. The jpeg compression will reduce file size and if you are editing in 16Bit Colot converting it to Jpeg 8bit color will half the file size. You do not want to save a layered file they will be large. If you insist on submitting a 16 bit color image save a Tiff but not a layered one. And save it with compression. If you have a large number of pixels you would most likely have the document Print resolution set much higher the 96PPI. So the print will not be huge be more normal in size like a high quality 8" x 10" print. A 8"x10" 300ppi image has a width of 2400px and a height of 3000px. A 3:2 Aspect Ration Raw image from my 16MP camera has an image 4896px by 3264 px and prints 9"x6" with a 544PPI. The bulk of an image files size is Pixel data, How well the pixel data in an image will compress depends on Image content. How much detail the image has. A blue sky will compress very well a cloudy sky will not compress as well there is a lot more detail to that sky.