I have been a passive user of dropbox, for the past few years… Someone shares a drop box with me and I set it up to connect from my desktop and forget about it.
But recently a client came to me with a few questions about Dropbox. They wanted to know if they could easily and safely share folders on drop box so clients could view them, but not edit them (There were a few more request from them but I will start with that one)
This write up will see how this question can be answered, also I will set up a new drop box account.
For those new to Dropbox
You can think of Dropbox as a shared hard drive in the cloud. You can put your files in it and access them via the web or other tools, you can also share your drop box with other people. There are corporate accounts you can share with a large team, etc.
Dropbox offers a free account but limits it to 2 GiB of data.
Starting your trial
Go to https://www.dropbox.com/ 
Click on the "Sign Up" button
Enter your First Name, Last Name, email address, password (You want to use for your Dropbox account)
Checkbox the "I agree"
Click Sign up.
I am on a Win 7 machine. DropBox auto downloaded an Dropbox executable file. I imagine on a Mac machine it would download an OSX compatible installer.
For the moment I will not use the installer, I will use the web site.
Open the Dropbox web interface
Open http://www.dropbox.com 
Since you just created this account it should auto log you in, forwarding you to a secure address like https://www.dropbox.com/gs
Here is the login page I see.
Create a folder and put some documents in it.
Click on Files
Here is my dropbox folder. Looks like I have a GettingStarted.pdf in my Dropbox folder.
Click on the New Folder icon.
A new folder pops up. Give it a name. I called mine test
The Test Folder is created. Click on it to open it
Loading files (via the web tool)
It looks like the Dropbox site supports dragging and dropping of files into it.
Here I grabbed a file from my computer and dragged it over the Dropbox web interface and dropped it.
It uploaded just fine.
It also supports uploading multiple files at the same time.
I dragged and dropped 8 files at once, it takes a little bit to upload them all. You can see the progress at the bottom of the screen. For example in this picture it shows 7 files left to upload.
As a test I tried dragging and dropping an entire folder that itself contained files.
It created the folder and uploaded all the files correctly.
OK, I have some files in a folder how do I share them?
Dropbox goes over their different was of sharing at
First lets go over "Share Link"
Right click on a folder and select "Share link…"
A new window opens that shows all the files and subfolders in this folder.
Click on "Share" in the upper right to share all files and folders in this folder.
Dropbox needs to verify you. Click Send email.
Check your e-mail and click Verify you email.
Click Share again.
Enter the emails of the people you wish to share this folder with and click send.
The user you sent the email to will now get a unique URL sent to them that they can use to open this folder via a web page.
The client (the persons email you used to share this folder with) will see this in their email
If they click on it
A new tab will open that is the folder you shared.
The client can view or download any file.
The client could click on Download and select Download as .zip to grab all the files at once.
Also if they want they could click on "Add to my Dropbox" This would add the files to their drop box (if they own one)
This link allows the client to see and download the files, but they cannot delete, edit, or add any of their own files.
As long as the link is shared anyone who has the URL (address) can open it up and view the shared files.
Removing the shared link
From the main menu click Links
All your shared links will be displayed, what is shared and when it was created.
Click the x button to delete the link
This message pops up. Click Remove Link
Now going back to the same URL gets you a 404 error.
Inviting people to a folder
What about inviting people to a folder? What is the difference from sharing?
The big difference is an invited user has permission to edit files and folders in the folder you invited them to.
Invite someone to a folder
Click on Invite to Folder
Enter the email of the user to share with.
Uncheck "Allow members to invite others" Since we do not want to give them the permission to share you folders to a third party.
The folder now says it’s a shared folder and the icon for the folder has changed to indicate it is being shared.
The invitee will get an email like this one.
They need to click View Folder.
The client will see this. They need to login to their own drop box account or create a new one so they can view the contents.
I filled out the information and created a new account and clicked "Create Account"
This page opens up.
To access the files via the Dropbox web site they need to click on Dropbox website.
And now they can see the folder and all its contents.
As a "Shared" folder this "invited user" is free to delete, modify, or add files.
So make sure you want them to have this level of priveleges before you "Share" a folder or file with someone else.
Stop sharing a folder
To stop sharing a folder…
Click on Sharing
Click on Options for the shared folder
You can click "Unshare Folder" to no longer share the folder with any other user.
Or you can, alternatively, click on any user and click "Kick out" to unshared with that particular user.
Also from this page you can invite more people to share the folder with.
As a side not, If you invite someone and they have not yet accepted that invitation you will see that they are in the "Still waiting" state, you can still uninvited them.
 Dropbox web site
 How do I link to a file or folder?