Separate each line of text with <CR><LF> (carriage return/line feed) sequence:
VB style: OSSMTP.MessageText = "This is " & vbCrLf & "a multi-line" & vbCrLf & "message"
C style: OSSMTP.MessageText = "This is\r\na multi-line\r\nmessage";

Component can't establish session with SMTP server I've specified.

1. Make sure SMTP Component has access to network. Check your firewall, anti-virus (or any other application, restricting access to network or Internet) settings.
2. Check connection properties (server name and port).
3. Check authentication properties - username, password. Most mailservers require authentication before accepting messages for delivery. On top of it some mailservers (namely, GMail and Yahoo Mail) require secure sessiion - TLS/SSL.

When I try to add SMTP Component to my project references, I keep getting a message saying something about name conflicting with existing library.

Most likely you already have a reference to a different library with the same name or older version of SMTP Component. The easiest way to resolve naming conflict would be Registry cleanup: make a search on 'ossmtp' value, delete all keys found, re-install SMTP Component

How do I integrate SMTP Component with MS Exchange?

You can only use SMTP Component to send emails. To get an access to other features of Exchange you need to use MS MAPI controls and/or Exchange object library.

When I ran setup I got 'OSSMTP_Setup.msi is not a valid Win32 application' message

Most likely you have incomplete download. For example, download in web browsers sometimes stops without any notification (due to time-outs or network problems). This file should be about 600 KB. If the installation package is smaller - try to re-download it

Where can I get more information about SMTP?

Read SMTP RFC

How do I send email to multiple recipients?

Use comma-separated list:
SMTP1.SendTo = "orders@mycompany.com, admin@mycompany.com, info@mycompany.com"
or
SMTP1.SendTo = "<orders@mycompany.com>, <admin@mycompany.com>, <info@mycompany.com>"
or
SMTP1.SendTo = """Sales Department"" <orders@mycompany.com>, ""Administrator"" <admin@mycompany.com>, ""Helpdesk"" <info@mycompany.com>"

What's the correct format for Timestamp property?

dd mmm yyyy hh:nn:ss +0000
Where yyyy is 4-digit year, mm - 2-digit month, dd - 2-digit day of month, hh - 2-digit hour, nn - 2-digit minutes, ss - 2-digit, +0000 - time correction between your local time and GMT in +/-hhmm format.
Example: 11 Feb 2005 16:03:05 -0500