Hello I have the following screen:
How can I indicate to users that they can click on each row of the table to open up another screen?
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The Material Design guidelines specify that rectangular colored need to be raised to prevent exactly the kind of confusion you are encountering. Otherwise it's not clear to the user that the button is an interactive element (can be pressed).
You can add a drop shadow to make the buttons raised and compliant with Material Design. This will also solve your affordance problem by making it clearer to the user that it's a button:
Also, the text in the buttons should really be centered, and unless there is some weird reason, the buttons should have the same width for consistency.
If you're using Material, then the answer is in Material itself. See http://www.google.com/design/spec/components/list-controls.html#list-controls-types-of-list-controls and specifically the "Expand/collapse" section.
Also, as we're using Material, remember to set a Primary color and an accent color, then build your palette by adding white or black to that color.
See below image taking your button color as primary color
Of course, this doesn't mean that you will need to use these colors. What it means is that if you want to use Material, then take a look at Material specs. They'll help you with a lot of aspects, since these concepts addresses a lot of design and usability issues and are tested by billions.
And the main part of these concepts: nothing is random in Material. Absolutely nothing (including your font sizes, padding, margins and so on)
Something as simple as a List might be your best option here.
You can do something similar to what @onofre-pouplana has mentioned above in which clicking on a list item will expand the list item to take over the whole screen. Obviously you would want to do some animation to make it look good and to give the user an understanding of what is happening.
Below is a look at what the list may look like, it's a very crude example but you will get the idea.