Not sure if you're asking how to create and use a database in Android, or online, so I'll try to answer both.
SQlite is the default embedded database solution in Android. You have two options here, but I'll go ahead and advise you to choose the former.
First option is to do it, as they say, "close to the metal" as possible. This means implementing your own contentprovider, your table structures, and all that. Here's a very nice tutorial on how to do just that.
Second option is to use an abstraction layer or whatever you want to call a library that does the heavy lifting and makes you stay away from coding the boilerplate stuff. There's a lot of choices out there, and each one differs in many ways -- some of them doesn't even use SQlite underneath. I suggest you take a look at this stackoverflow thread that lists some of the better persistence abstraction solutions available in Android.
Now for your question about storing stuff online -- if I understand correctly, what you want is a cloud server/solution setup. There's also quite a lot to choose from, and I'll let the other answers tell you what they are, but I personally recommend Parse. Storage is just one of the many useful features that it has, plus it also provides an Android API that simplifies all your network queries and result handling so that you don't have to deal with HttpConnection and JSON parsing. Plus it's free for small projects.