In Medellin you can find an array of furnished rental apartments ranging from budget to luxury. You will find that 90% of rental apartments are located in El Poblado, simply because that's where nearly all tourists wish to stay. Most rentals include gas, electricity, internet and cable tv service. It may also include maid service once a week to clean the apartment and wash the bedding / towels.

According to Colombian law rental apartments are subject to a minimum 30 day rental period unless the building has specifically obtained approved from the entire building and registered with the government. Despite this, many agencies/landlords overlook this rule and hope the neighbors don't complain. However recently the government has been sealing many illegally rented apartments, so book with caution. 

The most common places to search for rentals is Airbnb, Booking.com and Tripadvisor. These sites all have rating options so you can check the opinions of other people before making a decision. 

If you're staying longer term and want to rent a unfurnished apartment you'll probably head straight to a local agency. This is where you'll encounter many barriers. First of all you will need to find two people to guarantee the rental (called fiadores), they will need to have property in Medellin and a high income. Alternatively you will be asked to deposit 6 months rent in a bank account as insurance and complete loads of paperwork. For this reason most foreigners either chose to rent furnished apartments through foreign owned agencies or do it the hard way by trying to find an apartment owner willing to rent direct without the intervention of an agency.