How hard is it to start a career in civil engineering?

Getting some experience will be very helpful, both for the resume but also to see if it is really what you want to do. Get some exposure so that you can better understand what aspects you like about civil engineering and what you want to do. Being able to articulate these interests in an interview will help you express your interest in doing this.

I cannot speak specifically for civil engineering, but for electrical, mechanical (which is similar to civil) and biomedical engineering it is relatively easier to start a career with a Bachelors degree than some other majors.

For civil engineering you might consider taking the FE exam (fundamentals of engineering exam) during your senior year. This exam is especially important for civil and mechanical engineers since it gives you a standardized test and eventually a full license if you also take the PE exam later.
Read more about http://ncees.org/exams/fe-exam/

During your sophomore and junior year look for internships in your field during summer as this will give you experience and build your resume and increase your chances of finding a good career right of college.

Today you can look at a few of the popular job sites, monster.com, careerbuilder, Indeed.com and search titles like "civil engineer" and you should get a feel for how many opportunities there are for engineering jobs in general.

The marketplace for Civil engineering, like almost all engineering disciplines, is in need of more graduates. If you get high marks, participate in some interesting extra-curriculars or leadership roles, and can score a summer internship or two, you'll be in a great position to land a job right out of college. The internships will also give you real world experience which in addition to being looked at favorably by employeers, will also help you determine what you like (and don't like) about the civil engineering field.