It definitely depends on your university. My understanding is you must pick a major, but picking a minor is optional. The number of credits you need to complete to graduate will remain the same regardless. If you have completed all the classes required for your major, you may use the remaining credits freely (i.e take any class you want).
I believe cost wise, you will not be subject to additional costs for picking a major or minor. Effort wise, you would need to plan out your courses to ensure you can meet all the requirements for your major and minor to graduate on time.
I would strongly recommend you to discuss this with your university’s career advisor as different universities have different policies. If you are not sure of your interests, you may want to explore universities with schools of individualized studies where students can freely create their own major/academic plan with guidance from a career advisor. I have included the list of colleges below.
Hope this helps!
You don't have to pick a major or minor right away. In many cases the first couple of years of college you are taking prerequisite courses before you actually begin taking courses for your major. I would say during your freshman year of college start taking some courses that you may be interested in and also some career courses. This will help you decide on a major and ultimately what career path you may want to pursue.
First of all, echoing Julietta, I would highly recommend going into college open-minded. I'm from the USA, so if you're not quite sure what you want to study, you can pursue a general education at a local, 2-year college to obtain an Associate's degree (no requirement to declare a major). This would give you time to choose your classes and study subjects that you might be interested in, without committing to a specific major or minor. And those credits can be transferred to a different school, if you do want to finish a four-year college education. If you're interested in starting directly at a four-year college, again I'd still recommend taking a few general education classes your first quarter or semester, to figure out what it is you want to study.
At a typical four-year school, by the time you're at the end of your 2nd year, or start of your 3rd, most colleges will expect you to have chosen a specific major (and any minors). This is because you'll need at least 1.5-2 years to fulfill all the requirements mandated by the major and minor fields, and the school will want you to graduate on time. Bear in mind that wanting to pursue additional majors and minors is not inherently prohibited; it really just means you'd need to take more classes and obtain more college credits to fulfill the major/minor requirements. Every school has different requirements, and as Laura pointed out, some schools allow you to customize your path to a specific major/minor. So if this is something you're concerned about, definitely ask ahead of applying!
This summary doesn't include expedited/specialty programs offered at some universities (i.e. direct admit nursing programs, some combined undergraduate/masters programs, business school requirements, etc.); however, this should give you a good starting point in understanding majors and minors, and the time/cost needed to achieve those.
Hope this helps!