To be able to have your wordpress blog on your website homepage as appose to a different directory such as http://sitename.com/wp without using redirection or an enter page, you need a few steps and a code.
Please Note I’d recommend backing up files before making any large changes to WordPress settings just encase it goes wrong.
1) Open your index.php file (or your website homepage).
2) Insert the following code into it.
Change the WP to whatever your wordpress directory is.
3) Login to wordpress and go to Settings > General.
4) Change your blog address to the index page of your website. (to http://sitename.com/ replacing ‘sitename’ with your site name).
5) Then it should appear on your homepage.