Twitter uses OAUTH2. Basically it is something like this:
+--------+ +---------------+
| |--(A)- Authorization Request ->| Resource |
| | | Owner |
| |<-(B)-- Authorization Grant ---| |
| | +---------------+
| |
| | +---------------+
| |--(C)-- Authorization Grant -->| Authorization |
| Client | | Server |
| |<-(D)----- Access Token -------| |
| | +---------------+
| |
| | +---------------+
| |--(E)----- Access Token ------>| Resource |
| | | Server |
| |<-(F)--- Protected Resource ---| |
+--------+ +---------------+
Figure 1: Abstract Protocol Flow
The abstract OAuth 2.0 flow illustrated in Figure 1 describes the
interaction between the four roles and includes the following steps:
(A) The client requests authorization from the resource owner.
The
authorization request can be made directly to the resource owner
(as shown), or preferably indirectly via the authorization
server as an intermediary.
(B) The client receives an authorization grant, which is a
credential representing the resource owner's authorization,
expressed using one of four grant types defined in this
specification or using an extension grant type. The
authorization grant type depends on the method used by the
client to request authorization and the types supported by the
authorization server.
(C) The client requests an access token by authenticating with the
authorization server and presenting the authorization grant.
(D) The authorization server authenticates the client and
validates
the authorization grant, and if valid, issues an access token.
Above is an exceprt from spec
Please read through this . There are already sample code in various languages there. And here is a sample code for iphone/ipad