There are many strategies for beating writer's block. Not every strategy works for everyone, so experiment to find out what works for you. Keep in mind that different strategies may work at different times. What works for you today may not work for you next month, or even tomorrow. Here are a few strategies that have worked for me.
1) Word Mapping (also known as mind mapping or mindmapping or brainstorming)
For this strategy, I prefer to use pen and paper. (It can be done on a computer.)
To begin, write a word (or phrase) in the middle of the paper. Any word, even 'word' itself. If you have an idea for a story already, or are in the middle of a story, try to use a word or phrase related to what you're writing. Draw a small circle around it. You don't want the circle to obscure any of the letters, but you also don't want to make it too big. Leave yourself room to write around it, all the way around it.
Now, write down any other words or phrases that come to mind, related to the central word or not. For those words that are related to the central word, circle them and draw a line between the two circles. Words not directly related to the central word may be related to one of the other words. Draw lines between related words. Words that don't seem related at first glance are most likely related to something else on the page, though the relation may be obscure. If you can't think of any way it could be related to another word or phrase, just ignore it for now.
Next, choose one of the offshoots from the central word. Repeat the above process using this new word as the central word. By the time you finish this, you may have an idea of where to start (or continue) your story. If not, try repeating it for another offshoot. If you finish this process for every offshoot and are still stuck, it's time to try something else.
2) Free Write
This works equally well on computer or pen and paper.
I prefer to start this much the same way I start a word map. However, don't write the word or phrase in the middle of the page. Write it at the top.
Now, set a timer for five minutes (or one minute or ten minutes, whatever you feel comfortable with). Tell your inner editor/critic to take a hike. While he or she is gone, start writing. Write anything and everything that comes to mind. Even if you start out with 'I don't know what to write about. I don't know what to write'. Just get words down on the page. Let your subconscious have free reign. The important thing is getting words down on the page.
When your timer goes off, you should have some idea of where to start or where to go. If not, try something else. This next one always works for me.
3) Do Something Else
Put away your pen and paper, close your laptop, or shut your computer down. Put it in a different room, or at least under something where you can't see it.
Now, do something else. Go for a hike. Walk your dog. Play a video game. Call your mother. Pursue a hobby. Whatever. Just spend at least half an hour doing something not related to writing. Or reading. My preferred 'something else' is crafts. I either work on a cross stitch project or make something with beads. On occasion, I may draw or color instead.
While you are doing this something else, your subconscious mind will be working on your problem. It may only take half an hour. It may take a couple of days or even weeks (hopefully not), but once your subconscious figures it out, it'll let you know. Somehow. I've no idea how this works, but it does.
There are many other strategies for beating writer's block, but these three work best for me. With any luck, one - or more - of them will work for you too.