Which REST operation (GET, PUT, or POST) for validating information?

I recommend using a ValidationResource and two requests. Each instance of this resource represents the validation of a set of data. The workflow:

1. Create new ValidationResource

• Request: POST /path/to/validations
  • data to validate as the body
• Response: 201 Created
  • Location: /path/to/validations/<unique-id-of-this-validation>

2. Look up result

• Request: GET /path/to/validations/<unique-id-of-this-validation>
• Respons: 200 OK
  • body: {'valid': true} or {'valid': false}

This is a RESTful approach in which the Validation is a Resource with server state.

I use the same scenario as you and use PUT for it. You have to ask yourself: "when I send the same request twice, does this make a different state on server?" If yes, use POST, if no use PUT.

Google proposes use of Custom Methods for REST API

For custom methods, they should use the following generic HTTP mapping:

https://service.name/v1/some/resource/name:customVerb

The reason to use : instead of / to separate the custom verb from the resource name is to support arbitrary paths. For example, undelete a file can map to POST /files/a/long/file/name:undelete

Source: https://cloud.google.com/apis/design/custom_methods

So for validation the URL should be POST /resource:validate

My users enter a few information fields in a iOS app. This information must be validated on my server, which has a RESTful API. After validation the UI of the iOS app changes to indicate the result....I'm not getting a resource, and neither is a resource created or updated.

Since you aren't saving anything (not modifying any resource), I'd think this is technically more RPC than RESTful to me.

The following is my opinion, so don't take it as gospel:

If the information is simply being submitted and you're saying yes or no, and you're not saving it, I'd say POST is fine..

If information were actually being saved / updated, then choosing the proper HTTP method would be a lot more relevant.

POST = CREATE / SUBMIT (in an RPC context)
PUT = UPDATE (or CREATE if there is nothing to UPDATE)