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How to save number of times a user has tapped on a view

I am designing a simple application that will count how many times a user has tapped on a imageView. My question is what would be the best way of saving and reading this file. Any suggestions? I am thinking something like using Parse.com's local database. I have tried it, but I could not get it working the way I wanted. I am still a beginner, so please not so fancy suggestions.

Try to save data in SharedPreference. SharedPreference works like database for application on device that will be stored until any one has unistall app from device.
To create sharedPrefernce-
SharedPreferences prefs = this.getSharedPreferences(
"com.example.app", Context.MODE_PRIVATE);
To store data -
prefs.edit().putInt("key", int_value).apply();
To retrieve data-
// use a default value
int l = prefs.getLong("key", default_value);

Simplest options is always thebest option, go with shared preferences
Here is simple tutorial from google http://developer.android.com/training/basics/data-storage/shared-preferences.html
It will store your data in application local file. Take a note of that there are different shared preferences in example getPreferences() will return file specific for activity you used this method. While getSharedPreferences() will return application global file.

Is it possible to save a variable value in Android (in memory), even after closing the application? If so, how?

How is it possible to save a variable value in an Android app? Can the value be saved in memory? I am planning to save a float value in my application, so the next time the app is opened, the previous value will be loaded. How do I go about this? Shared Preferences or something else?

Yes. SharedPreferences is the best available option.
To store float value:
SharedPreferences preferences = PreferenceManager.getDefaultSharedPreferences(context);
SharedPreferences.Editor editor = preferences.edit();
editor.putFloat("storedFloat", storedFloatPreference); // value to store
editor.commit();
Also check this: http://developer.android.com/reference/android/content/SharedPreferences.Editor.html#putFloat(java.lang.String,%20float)
Check this SO question. It nicely answers your question: How do I get the SharedPreferences from a PreferenceActivity in Android?

Yes its possible use shared preferences.
http://developer.android.com/reference/android/content/SharedPreferences.html
http://developer.android.com/guide/topics/data/data-storage.html#pref
You can also use sqlite data base to store the data and retrieve when you need it.
Your other storage options. you could store your values to a file in memory.
http://developer.android.com/guide/topics/data/data-storage.html

Look at the Storage Options Docs to be sure you pick the most appropriate type for you but if its just one value then SharedPreferences should work fine for you.
See The Docs for a good example on how to use SharedPreferences

Saving Shared Prefrences in Multiple instances

I would like to be able to save my users session or sharedPrefrences in a way that if the user kills the application and you start it it would look like this.
Button one = Start Activity with Blank Preferences
Button Two = List of Saved Sessions of Preferences and once clicked all put into the Starting activity.
Is this possible and if so how would I go about doing that?
Thank you!

Yes you can do that and it is good to use sharedPreferences if you just have to store some session variables. But if it is more, then go for database.
Do clear sharedPrefences in your application you need to do this:
SharedPreferences settings = PreferenceManager.getDefaultSharedPreferences(activity);
Editor editor = settings.edit();
editor.clear();
editor.commit();
For reading the preferences, you can keep a sharedPreference with the count for the seesions. While saveing the prefences, always save with the strings session1, session2, session3 etc. So, while accessing them based on count, prepare a loop and form the string and access all the session variables and show them.
The reason why I didnt suggest you to do getAll() for sharedPreference is that, you may save few other things in sharedPreference. So by forming strings yourself, while reading you can just get the sessions and not other data saved in sharedPreference.
I hope you understand what I meant

Is this possible
I would say yes, depending on exactly what you mean.
if so how would I go about doing that?
SharedPreferences has a couple different functions to do something like this, depending on exactly what you want. You can get a Map of all preferences that are stored after clicking Button2 with getAll() or a set of preferences with a certain String such as "userName" or something similar with getStringSet(). Play around with the functions it offers and see if it gives you what you are looking for.
Also take not of the warnings of these functions
Note that you must not modify the set instance returned by this call. The consistency of the stored data is not guaranteed if you do, nor is your ability to modify the instance at all.

How to attach a Preference to a particular SharedPreferences?

I am working on implementing the preferences for our application. I know how to display preferences UI and how to read/write values using SharedPreferences. In our app, I need to handle two sets of preferences and I would like to ask about this issue, one comment in the Android documents in particular.
The documentation for Preference.getSharedPreferences() has the following comment under the Return values section:
Returns The SharedPreferences where this Preference reads its value(s), or null if it isn't attached to a Preference hierarchy.
I would like to ask how it is possible to attach a SharedPreferences to a particular Preference, be it EditTextPreference or others. In other words, how does the persistence code in a Preference know that it should store the user input in one particular SharedPreferences object and not the other?
To explain my question further with an example, suppose I have the following:
SharedPreferences prefs1 = getSharedPreferences(file1, mode);
SharedPreferences prefs2 = getSharedPreferences(file2, mode);
My question is what API I should use so that prefs1 is used by the Preference objects' persistence code and not prefs2.
The target is Nexus One, running 2.3.4.
Maybe the answer is obvious but I could not find it after reading the documentation and searching the web. Thank you in advance for your help.

In other words, how does the persistence code in a Preference know that it should store the user input in one particular SharedPreferences object and not the other?
Preference uses PreferenceManager's getSharedPreferences(), which eventually routes to getDefaultSharedPreferences().
You are welcome to create your own Preference subclasses that change this behavior, but since the preference screen system may not be designed to handle multiple SharedPreference objects, there's a chance that your preference changes might not get persisted.
IOW, I encourage you to reconsider:
In our app, I need to handle two sets of preferences

android How to detect if the application have run in the past

I would like to know if and how it is possible to detect if my application have run in the past on a given android device. I would like every time the phone reboots to be able to check if my application has run on the past and retrieve some private data. If not just create those data.

You could store a simple value in the SharedPreference of the application.
insert this into your onCreate() in your Main Activity
SharedPreferences shared = getSharedPreferences("config", 0);
if (shared.getBoolean("hasRunBefore", false))
{
// have run before.
}
else
{
SharedPreferences.Editor editor = shared.edit();
editor.putBoolean("hasRunBefore", true);
editor.commit();
// have not run before
}

As others have said, the easiest way to read and write this information is in the SharedPreferences. However, you said you want to do this every time the phone reboots. The way to go about that is to implement a BroadcastReceiver and register to receive ACTION_BOOT_COMPLETED message, and make sure to add a permission to your manifest for RECEIVE_BOOT_COMPLETED.
http://developer.android.com/guide/appendix/faq/commontasks.html#broadcastreceivers
http://developer.android.com/reference/android/content/Intent.html#ACTION_BOOT_COMPLETED
http://developer.android.com/reference/android/Manifest.permission.html#RECEIVE_BOOT_COMPLETED

Check if this data exists ? Or put something in the default PreferenceManager of your application

You'd save everything using SharedPreferences. This will create a file readable by your app that will be created when first written to.
See the following:
Tutorial
Documentation