If you are using your own phone for a US or EU rental you might have to set up your APN Setting manually

Galaxy/Android:  Go to Settings->More Networks->Mobile Networks. Turn Mobile data and Data roaming - on. Select Access Point Names and Add New APN.
Fill in the “Name” field and the “APN” field, see below. (For other phone models, steps may vary.) 

iPhone: Your internet should work automatically. If not, go to Settings->Cellular. Then Enable 3G and Enable Data Roaming. Select Cellular Data Network.
Fill in the “APN“ field, see below.

Put in the details below based on your provider. (The APN field is case sensitive.)
Leave everything else blank 

For T-mobile:
      for Android (OS):
                         Name: TMobile
                         APN: fast.t-mobile.com
      for iPhone:
                          APN: fast.t-mobile.com

For AT&T:
      for Android (OS):
                         Name: NXTGENPHONE
                         APN: NXTGENPHONE
      for iPhone:
                         APN: NXTGENPHONE

For Ultra:
      for Android (OS):
                         Name: ultra
                         APN: wholesale
      for iPhone:
                         APN: wholesale

For Lyca:

      for Android (OS):
                         Name: Lycamobile
                         APN: data.lycamobile.com
      for iPhone:
                         APN: data.lycamobile.com

For Net10:
      for Android (OS):
                         Name: Net10
                         APN: RESELLER
      for iPhone:
                         APN: RESELLER

For Simple:
      for Android (OS):
                         Name: Simplemobile
                         APN: simple
      for iPhone:
                         APN: simple

For H2O:
      for Android (OS):
                         Name: h2o
                         APN: PRODATA
      for iPhone:
                         APN: PRODATA

For Three (UK):
      for Android (OS):
                         Name: 3
                         APN: three.co.uk
      for iPhone:
                         APN:three.co.uk

For Gifgaff (UK):
      for Android (OS):
                         Name: giffgaff
                         APN: giffgaff.com
      for iPhone:
                         APN:giffgaff.com