You may already be aware of the technique of sentence mining and incorporating it into your daily studies. Sentence mining is great and should be a major part of most people's Chinese learning. Sentence branching is a complementary technique to make it even better.
To use sentence branching, you need an initial seed sentence and a good bank of example sentences. Most Chinese dictionaries offer example sentences, and other good sources include 句酷 and Tatoeba. All you do is go through the sentence word by word; for each interesting word, you look up example sentences and add some to your learning deck.
What makes a word interesting is up to you, but I at least add new words or words that I've previously struggled to recall. Adding every 实词 (content word) in the sentence is also good. You can of course add a new sentence for every word in the seed sentence. There aren't any particular rules for sentence branching.
As an example, if you have this seed sentence:
You might add the following branch sentences to your deck:
That would probably be enough, but if you're looking for more sentences, you can then go through each of the branch sentences and use it as a seed sentence to repeat the process. In this way you can very quickly build a web of related vocabulary represented in effective sentences (more on that below).
Notice how the last branch sentence managed to include a pair of words from the seed sentence: 任何困难. This is also good as it lets you reinforce what appears to be a collocation between these words.
Branching out from your textbook
A major advantage of sentence branching is that it's a great way to discover and explore new vocabulary, grammar structures and idioms without needing a pre- designed course or textbook. With sentence branching, you can start with one fragment of Chinese and expand it into as much new learning material as you need.
You don't need to start from a sentence or word in your learning deck either. You can simply open up any Chinese website, book or other material and pick out words and sentences that interest you. Due to the expononential nature of sentence branching, this can quickly supply you with more new learning material than you'll ever be able to finish, which is a good thing.
A web of memory
Another great thing about sentence branching is that it naturally produces interconnected learning material. Fluency and authenticity are improved because you're able to effectively link your knowledge of the language together rather than trying to juggle isolated pieces.
This linking effect does occur naturally with any learning, but it's great to take opportunities to promote it as much as you can. Sentence branching provides an easy and methodical way to do that.
Aside from that wider effect on your Chinese, sentence branching is also a good way to deal with leeches. Leeches are things you're trying to learn that just don't seem to stick and keep slowing you down. Try using sentence branching to build a web of related material around a leech and see if it works for you.