Many hotels (even very small, rural ones) offer free WiFi and so do many cafés. If an internet connection is important to you it's best to check when you book your accommodation.
If you want to use your own mobile phone service to access the internet note that 4G is not widely available in Crete. On the other hand you will get a 3G connection (of variable quality) in most places frequented by tourists.
It is also possible to buy short term mobile internet connections with Cosmote or Vodafone. Their offers and rates change constantly so best check on their web sites (both have English versions) to find something suitable.
If you don't have a tablet, laptop or smartphone you'll need to look for an internet café. Popular until recently they are getting more difficult to find because less people need them.
If you plan to live in Crete longer and want a fixed ADSL line bear in mind that this is not available everywhere. It's generally not a problem getting a phone line in cities but in some rural areas it is difficult (and sometimes impossible) to get a phone line. In other areas the quality of the lines is too low to support an internet connection. Things are getting better all the time and the areas without connectivity are shrinking but if having a fast internet connection is very important to you it's probably a good idea to do a bit of research before deciding where you will settle down. Ask locals and check with the OTE phone company.
If you live in area with poor mobile signal and no ADSL lines your last option is satellite internet. This has become faster and a lot more affordable so all is not lost.