VK SDK allows you to authorize user without asking him to enter login/password. After that you can call any API methods.

https://github.com/VKCOM/vk-ios-sdk 

To use VK SDK primarily you need to create a new VK application here by choosing the Standalone application type. Choose a title and confirm the action via SMS and you will be redirected to the application settings page.
You will require your Application ID (referenced as API_ID in the documentation). Fill in the App Bundle for iOS field. 
To use authorization via VK App you need to setup a url-schema of your application.

• Xcode 5: Open your application settings then select the Info tab. In the URL Types section click the plus sign. Enter vk+APP_ID (e.g. vk1234567) to the Identifier and URL Schemes fields.

• Xcode 4: Open your Info.plist then add a new row URL Types. Set the URL identifier to vk+APP_ID

CocoaPods is the dependency manager for Objective-C, which automates and simplifies the process of using third-party libraries like AFNetworking in your projects. See the "Getting Started" guide for more information.

Podfile

pod "VK-ios-sdk"

Add the sdk/sdk.xcodeproj file to your project. In the Application settings open Build phases, then the Link Binary with Libraries section. Add libVKSdk.a there, then import the main header.

#import "VKSdk.h"

Source Code on GitHub

1) Put this code to the application delegate method application:openURL:sourceApplication:annotation:

-(BOOL)application:(UIApplication *)application openURL:(NSURL *)url sourceApplication:(NSString *)sourceApplication annotation:(id)annotation
    {
        [VKSdk processOpenURL:url fromApplication:sourceApplication];
        return YES;
    }

2) Initialize SDK with your APP_ID for any delegate.

[VKSdk initializeWithDelegate:delegate andAppId:YOUR_APP_ID];
    if ([VKSdk wakeUpSession])
    {
        //Start working
    }

See full description of VKSdkDelegate protocol here: http://vkcom.github.io/vk-ios-sdk/Protocols/VKSdkDelegate.html

There are several methods for authorization:

[VKSdk authorize:scope];
[VKSdk authorize:scope revokeAccess:YES];
[VKSdk authorize:scope revokeAccess:YES forceOAuth:YES];

Generally, [VKSdk authorize:scope]; is enough for your needs.

When succeeded, the following method of delegate will be called:

-(void) vkSdkDidReceiveNewToken:(VKAccessToken*) newToken;

In case of error (e.g., user canceled authorization):

-(void) vkSdkUserDeniedAccess:(VKError*) authorizationError;

To get the User ID after authorization use method of VKAccessToken class:

[[VKSdk getAccessToken] userId] //Return NSString - authorized user id

Below we have listed the examples for several request types.
1) Plain request.

VKRequest * audioReq = [[VKApi users] get];

2) Request with parameters.

VKRequest * audioReq = [[VKApi audio] get:@{VK_OWNER_ID : @"896232"}];

3) Http (not https) request (only if scope VK_PER_NOHTTPS has been passed)

VKRequest * audioReq = [[VKApi audio] get:@{VK_OWNER_ID : @"896232"}];
audioReq.secure = NO;

4) Request with predetermined maximum number of attempts.

VKRequest * postReq = [[VKApi wall] post:@{VK_MESSAGE : @"Test"}];
postReq.attempts = 10;
//or infinite
//postReq.attempts = 0;

It will take 10 attempts until succeeds or an API error occurs.
5) Request that calls a method of VK API (keep in mind scope value).

VKRequest * getWall = [VKRequest requestWithMethod:@"wall.get" andParameters:@{VK_API_OWNER_ID : @"-1"} andHttpMethod:@"GET"];

6) Request for uploading photos on user wall.

VKRequest * request = [VKApi uploadWallPhotoRequest:[UIImage imageNamed:@"my_photo"] parameters:[VKImageParameters pngImage] userId:0 groupId:0 ];

[audioReq executeWithResultBlock:^(VKResponse * response) {
        NSLog(@"Json result: %@", response.json);
    } errorBlock:^(VKError * error) {
    if (error.code != VK_API_ERROR) {
        [error.request repeat];
    } else {
        NSLog(@"VK error: %@", error.apiError);
    }
}];

Every request can return NSError with domain equal to VKSdkErrorDomain. SDK can return networking error or internal SDK error (e.g. request was canceled). Category NSError+VKError provides vkError property that describes error event. Compare error code with the global constant VK_API_ERROR. If they equal that means you process vkError property as API error. Otherwise you should handle an http error.

Some errors (e.g., captcha error, validation error) can be proccessed by the SDK. Appropriate delegate methods will be called for this purpose.
Below is an example of captcha error processing:

-(void) vkSdkNeedCaptchaEnter:(VKError*) captchaError
{
    VKCaptchaViewController * vc = [VKCaptchaViewController captchaControllerWithError:captchaError];
    [vc presentIn:self];
}

VKCaptchaViewController
SDK gives a feature to execute several unrelated requests at the one call.

1) Prepare requests.

VKRequest * request1 = [[VKApi audio] get];
request1.completeBlock = ^(VKResponse*) { ... };

VKRequest * request2 = [[VKApi users] get:@{VK_USER_IDS : @[@(1), @(6492), @(1708231)]}];
request2.completeBlock = ^(VKResponse*) { ... };

2) Combine created requests into one.

VKBatchRequest * batch = [[VKBatchRequest alloc] initWithRequests:request1, request2, nil];

3) Load the obtained request.

[batch executeWithResultBlock:^(NSArray *responses) {
        NSLog(@"Responses: %@", responses);
    } errorBlock:^(NSError *error) {
        NSLog(@"Error: %@", error);
}];

4) The result of each method returns to a corresponding completeBlock. The responses array contains responses of the requests in order they have been passed.

Full manual about VK iOS SDK classes is here: http://vkcom.github.io/vk-ios-sdk/

Share dialog allows you to create a user friendly dialog for sharing text and photos from your application directly to VK. See the Share dialog usage example:

VKShareDialogController * shareDialog = [VKShareDialogController new]; //1
shareDialog.text = @"This post created using #vksdk #ios"; //2
shareDialog.vkImages = @[@"-10889156_348122347",@"7840938_319411365",@"-60479154_333497085"]; //3
shareDialog.shareLink = [[VKShareLink alloc] initWithTitle:@"Super puper link, but nobody knows" link:[NSURL URLWithString:@"https://vk.com/dev/ios_sdk"]]; //4
[shareDialog setCompletionHandler:^(VKShareDialogControllerResult result) {
    [self dismissViewControllerAnimated:YES completion:nil];
}]; //5
[self presentViewController:shareDialog animated:YES completion:nil]; //6

1) Create an instance of the dialog controller as usual.

2) Attach some text information to a dialog. Notice that users can change this information.

3) Attach images uploaded to VK earlier. If you want user to upload a new image, use the uploadImages property.

4) Attach link at your pages (supports only links attachment for now).

5) Set the dialog completion handler.

6) Present the dialog viewcontroller in your view controller.

VK SDK provides a special class for working with UIActivityViewController - VKActivity. See example below for understand how it works:

NSArray *items = @[[UIImage imageNamed:@"apple"], @"Check out information about VK SDK" , [NSURL URLWithString:@"https://vk.com/dev/ios_sdk"]]; //1
UIActivityViewController *activityViewController = [[UIActivityViewController alloc]
                                                    initWithActivityItems:items
                                                    applicationActivities:@VKActivity new]; //2
[activityViewController setValue:@"VK SDK" forKey:@"subject"]; //3
[activityViewController setCompletionHandler:nil]; //4
if (VK_SYSTEM_VERSION_GREATER_THAN_OR_EQUAL_TO(@"8.0")) {
    UIPopoverPresentationController *popover = activityViewController.popoverPresentationController;
    popover.sourceView = self.view;
    popover.sourceRect = [tableView rectForRowAtIndexPath:indexPath];
} //5
[self presentViewController:activityViewController animated:YES completion:nil]; //6

Let's see the steps of the example:

1) Prepare your share information - UIImage, NSString and NSURL. That kind of information may be shared throught VK.

2) Prepare UIActivityViewController with new application VKActivity.

3) Set additional properties for activityViewController.

4) Set completion handler for activityViewController.

5) Check if you're running above iOS 8. If user working with iPad, you must present the activity controller in popover, otherwise you'll get system error.

6) Present the activity controller as usual.