Good news! It sounds like this is pretty easy. I am assuming you are new to InfoPath and am starting with the basics, so forgive me if you already know some of this (if you have created forms before, skip to the workflow part below). What you will do is create a simple form and then attach workflow to it using the out-of-the-box workflow that comes with the SharePoint form library. I am assuming you are using SharePoint 2007 Standard. If so, this workflow is available and ready to go and just needs to be tweaked. If not, you will need to let me know, so we can pursue other paths.
First, you will need to create your form. You can do this by opening InfoPath and clicking Design a Form Template (on the left hand side.) Next, ensure that “Blank” template is highlighted and click Next.
Your new InfoPath form will look very bland – just a blank page. On the right hand side, you will choose a layout table (Table with Title is a good one to start with) and then give your table a title. Keep in mind that all formatting is similar to Word so you can make your form look nice by formatting the text. You will next expand the Controls section (At the top of the right column, use the drop-down box currently displaying Layout) and there you will find all you need to add function to your form. Where it says “Click here to add content” you can add your text boxes and drop down boxes for users to enter information by clicking in that form and then selecting the different controls.
When you have a control on the page, you will want to double click on it to configure it. For instance, each control is named because it can be reused. Its default name is “field1” and that isn’t really intuitive. So if your first control is a text box that will hold a user’s name, you may want to call it UserName. (Note you do not want spaces or special characters.)
I am assuming your users will be saving this form to a SharePoint Form library. To publish to a form library, click File -> Publish. You will be asked to save the file locally before it is published. Next, it will ask you where you want the form published to. Choose SharePoint form library and click Next. Enter the URL of the location you want to store your form. The format will be http://<your SharePoint Server Name>/<your subsite>/. Click next. On the next page, choose Document Library and click Next and then Next again. Type a name for your library and a description and click Next. For columns to promote, you may bring in fields from the form to your SharePoint list. Once you do this, any information your users enter into these fields will auto-populate when the form is saved to the library. Choose what columns you want in your library and click Next and then Publish. You may also want to create a submit button for users to submit the form to the library. In the current format, your users will have to save it. Although that is easier for you as the form designer, keep in mind you will want them to save it with a unique name to avoid overwriting other requests in the library.
WORKFLOW - In your form library, click next and then Settings à Form Library Settings. In the center section, click on Workflow Settings options and select Approval workflow. Next, give the workflow a name and choose when you want your workflow to start. Probably you will want your workflow to start when a new item is created. Click the Next button. If your form needs to be approved in a specific order, choose Serial workflow. If you want your workflow to go to multiple people at once, choose Parallel workflow. Parallel workflow may be good in your case, since it seems like only one of a group of people need to approve this form. Then, when you add your approvers (these will be your Authorized Persons), add them in a group (Like a pre-created SharePoint group or an AD group) and choose the option to “Assign a single task to each group entered.” This way, if only one person needs to approve it from that group and does so, the form is then approved. If you let the users reassign tasks, it will let them push the form approval off to other users when they are busy. Set how long you want the group to take completing this task (parallel) or set how long you want to give each user to complete their task (serial). Then click OK and your work flow is ready to go. Try it out by creating a document and saving it back to the library. You will see a workflow column appear in the library. When you click on it, it will take you to a workflow status page where you can see what tasks have been created for your users.
Each task will be kicked off with an email to the person it is assigned to and the final approval will also be accompanied with an email.
Does this help at all? Please let me know if you need additional clarification.