Your iPhone can often behave like your Mac. It has full Web access through an iPhone version of Safari. You can also work with e-mail, even e-mail with attachments, in much the same way as you can with your Mac, with the help of applications you can purchase from the Apps Store.
Open your "Mail" Application on your iPhone and load your e-mail. Find an e-mail with an attachment and click on it. The "Mail" Application marks e-mails with attachments with a paper clip to the right of the name of the person who sent it. Click on the email to open it. If you have received an e-mail with just a picture attached and no text in its body, that picture will appear in your e-mail and fill the screen. Press and hold the picture. A pop-up menu with the following two options will appear: "Save Image" or "Copy." Press "Save Image" to save the picture in the "Camera Roll" folder in your Photo Albums that you can access by touching the "Photos" icon illustrated with a sunflower. Pressing "Copy" will only allow you to paste the picture into another e-mail by pressing any section of the body of an e-mail twice and clicking "Paste" from the pop-up menu. If there is text in an e-mail with a picture attached, or if the attachment is any other kind of file, you will find it at the end of the email in either a square or rectangle with an icon.
Press and hold the square or rectangle icon at the end of the email. If the attachment is a picture, it will load into your e-mail and fill the screen. You can save that image by pressing and holding the loaded image. Select "Save image" to save it into your "Photos" icon. If the attached file is a Microsoft Word document, your "Mail" Application will simply let you view it. Pressing and holding the rectangle with a W icon will open another screen filled by the attachment. If you just want to save the text itself and do not need to save it as a Word file, press and hold the screen wherever you want. A pop-up menu will appear. Click "Select All" and "Copy" in the new pop-up. Open your "Notes" Application, create a new note by pressing the "+" sign in the upper right corner, double-click the new note wherever you want, and click the "Paste" pop-up. The full text of the Word document will appear. You can change the text and save it in the "Notes" Application. You can also e-mail that text to yourself or to anyone. The text will appear in the body of the email, not attached as a Word document.
Purchase the "Documents To Go" Application if you want to save (as well as edit and create) Microsoft Word, Excel or PowerPoint documents onto your iPhone in their original format. You can also save and view Adobe PDF, Apple iWork, and other kinds of files. Only with the premium version of the program can you save (as well as edit and create) PowerPoint documents and save any of the three kinds of documents directly from your Gmail or Microsoft Exchange. With the regular version, you can save files onto your iPhone by connecting it via USB cord and activating the two-way file synchronisation that comes with the included Desktop Application. Any new file you have added to the "documentstogo" folder since your last sync and any changes made to the documents on your iPhone will be added and reconciled both on your Mac and your iPhone.
There are other applications available that enable you to save attachments directly from your e-mail much like your Mac can, but these Applications only run if you unlock, or jailbreak, your iPhone. Doing so will void your iPhone warranty.