How can I get a field's value from a global based on a url segment?
You will need to access a few things. 


The url segment you need (for example the last segment)
The global set name
The field handle name


You can use getLastSegment to access the last url segment.

Using the global set names above let's say I have a url like this:

mysite.com/first

{% set segment = craft.request.getLastSegment() %}  // first


I know I've got a global set called firstGlobalSet, and now I've got first. We just need to put them together. You can use Craft's 
getSetByHandle method to access the global set via its handle.

{% set global = craft.globals.getSetByHandle(segment ~ 'GlobalSet') %}
{{ global }} // firstGlobalSet


Now that we've got the correct global set, we can get to the field we need. In this case it's myTextField.

{{ global.myTextField }}