Here is a good example for how to ask for to be a guest author on another website:
I have been following your blog on websitename.com for a while. I can say without hesitation that you have done some remarkable work with informative content. I especially appreciated your article about Name-of-Article-Here. It was very helpful and I have already shared it with others. Moreover, I have noticed that you are accepting guest posts as well, so I thought of contributing my ideas to your blog.
I have done a comprehensive research on the topics that are related to your blog and can offer you an article which will help your readers immensely. It will not only attract more visitors but also help them get the informative stuff on the subject. Please let me know if you can accept my blog post.
I assure you that the content will be informative, relevant, unique, and will provide help to the blog visitors.
Furthermore, being a professional writer. I Hope for a positive and professional response from your side.
Thank you for your consideration and best regards,
Your email address
Your direct phone number
Straightforward and to the point. Give a little proof that you actually read the blog and provide more than a gmail email account to give proof.
I receive many requsts to be a guest blogger each week. Avoiding most agencies and freelancers, I hope to offer real entrepreneurs who have expertise and are in trenches an opportunity to get a little attention.
This is VERY important to you for your online marketing. If you have little or no activity off your website, if you are only working on and inside your own website, it will offer very little chance of making an impact.
Just the same as a retail store... fix the shelves and sweep as often as you like, inside activity does not bring people in the doors.
You can now begin to reach out to webmasters, business owners and editors of other websites to make your request. Of course you will leave a link in your article back to your own website. If they accept it, include one link in the body and one link in the about section.
The good news; If you ask and someone says: "No thank you", there is a good chance they took a peek at your website to determine relevance and value. Someone just might also get curious enough and become a customer.
To get better results, make a stand, issue a declaration and change the way you do things. Create a revolution in your own self, reach out and be a guest author.