Is it easier of I do certain things myself?
There's always a chance that you will spend a lot of time doing something that your web designer can do in only a few minutes. Or, worse, that you create a problem that will take the designer a lot of time to correct. Whether that's a risk you should take depends on how much you value your time and who is paying for your designer's time.
There are some fairly simple tasks you might prefer to do yourself, and there are some things that are probably better done in-house, including:
Content development
If you have good in-house writers, or a marketing department that insists on a particular focus, you'll probably do a lot of the content development in-house. If there is a lot of content on the website, especially if it involves area expertise, you'll probably want to do it yourself. Some firms have good writers on staff, and writing for the web is a somewhat specialised skill, of course.
Logo, images, and graphic design
Perhaps you have something in mind, or maybe you have a well developed corporate identity. It's your website, it should be something that makes you happy. Many things that look cool to the untrained eye will come across as amateurish to someone who isn't already acquainted with your company. Consistency is important, though. If you have an image, your designer should work to ensure that website works with that image.
Website Maintenance
Once your site is done, it's tempting to do the updating yourself. Actually, this can be set up pretty easily by your website developer. Websites can be built on top of a Content Management System. What you want to avoid doing, unless you are a developer, is making modifications to the html yourself. Simple mistakes can cause very strange consequences that may not be easy to fix.

