How do I tell the DNS Manager to redirect my domain to a specific page on my website?

The DNS standards do not allow for this, so you will not be able to do this with the DNS Manager. Instead, you will need to setup Name-Based Virtual Hosts in your webserver.

You do need to setup an A or CNAME record in DNS so that www.example.com and example.com point to 203.0.113.0.

https://linode.com/docs/networking/dns/dns-manager-overview/#add-records

This guide will help you get this set up on Apache:

https://httpd.apache.org/docs/2.2/vhosts/name-based.html

For example in the scenario related to this question, we would have the following virtual host settings:

<VirtualHost *:80>
   ServerName www.example.com
   ServerAlias example.com
   ServerPath /example
   DocumentRoot /path/to/content
</VirtualHost>

@hphillips any plans on adding the same funtionality as cloudflare and dnsimple have
with a URL RECORD
https://support.dnsimple.com/articles/url-record/

So-called URL records are NOT STANDARD. They are a proprietary convenience invented by dnsimple.com that depends on a proprietary service. See:

https://support.dnsimple.com/articles/supported-dns-records/

Money quote:

We also created 3 proprietary record types:
 
ALIAS
URL
POOL

The emphasis is mine.

Also, at https://support.dnsimple.com/articles/url-record, it sez:

DNSimple exposes URL records as standard A and AAAA records. The canonical representation is the same for the A and AAAA records.
 
When you create a URL record, we automatically configure a set of A and AAAA records to point the source hostname to an instance of our redirector service. When an HTTP client queries the hostname, our redirector service serves an appropriate HTTP request to redirect the client to the target URL you configured in the record editor.

Again, the emphasis is mine. AFAIK, Linode doesn't have a proprietary "redirector service."

What dnsimple.com (and presumably cloudflare.com) are doing is violating the rules in order to make it "easy" for you. What are you gonna do if they raise their rates and you want to move your configuration someplace else? If the target of your migration doesn't have dnsimple.com's proprietary "redirector service," you are going to be seriously SOL and forced to figure out whatever spaghetti dnsimple.com has created for you (behind your back) to lock you in to them. No thanks…

-- sw

Totally agree with @stevewi. I use ClouDNS which also has a redirection service which whilst it is tempting to use as it is easy to configure (and less maintenance) there are drawbacks to simply doing the redirection on yourself (which if you have a website/Linode already, there’s no reason not to, you’re not forking out anything extra; you have everything you need already.)

Drawbacks include the lock-in as mentioned by @stevewi, and also a nasty “this is not secure” error message if someone accesses your redirected hostname with HTTPS (as the redirection service doesn’t have your SSL cert, and I don’t know any that allow you to set this up.)

Also you are not in control of this service - if the redirection service fails (but your DNS and Linode/website are still up) you’re still gonna lose visitors due to a circumstance outside of your control - it’s one more point of failure you don’t need.