The program fee is based on a matrix, currently located here. It ranges from $1,000 to $25,000 a year, depending on your "trailblazer score." Higher tiers cost more, but gain more benefits as a result. For example, higher tier partners will get better leads from Salesforce, more exposure in marketing material, etc. The actual process typically takes a few weeks to a few months, depending on how many applicants are currently in the queue, the size and complexity of the partner, etc. There is no exact measurement of how long it will take, but instead is variable as partners are added and renewed. You'll want to read the linked resources from the above link for specifics, as they vary from year to year in regards to training, certifications, etc.
The basic process is to get certified (you need a minimum number of certifications to become a partner), apply for partnership, fill out the required contracts, and pay the partner program fee. The programs provide free and discounted training, some free certifications, access to support, marketing referrals, and more, based on the matrices in the above link and the related links you'll find there.