Once individual notes can be read with ease, accuracy, and speed (the fastest you can accomplish, the better) the next part is learning (another word for memorizing) two note patterns. This is what psychologists call "chunking", grouping individual parts to form a larger part. This is simply chunking two individual notes together. In musician-speak, this is interval identification.
The mechanics can be first practiced without reading. Just practice playing two intervals with as many different fingerings as your hand can manage. Speed and accuracy count. It must be practiced until easy. This will automate the mechanics during reading so you don't have to think of how you'll play; you'll just play.
The reading is as before. Practice until it's easy, accurate, and fast. The faster, the better. Precision is also of upmost importance. Easiness indicates your movements are efficient and effective.
What great sight-readers have is a vast memory-base of various possible combinations of notes. When they see a score, they see the notes in large chunks. They essentially play from memory. The difference is the order in which they recall that memory, similarly to how you are reading this reply. You already know all of the words. The difference is the order that is being used to communicate my ideas.
In contrast, if I were to speak about an unfamiliar topic like neuroscience, the following sentences will be difficult to understand and pronounce because you don't have knowledge (another word for memory) of the terms:
The chemicals involved with neuronal communication include excitatory neurotransmitters such as acetylcholine, glutamate, aspartate, noradrenalin and histamine, and inhibitory neurotransmitters such as gamma aminobutyric acid (GABA), glycine, and seratonin. Dopamine functions as both an excitatory and inhibitory neurotransmitter and is essential for the formation of memory.
Notice that for the common words, you could understand but the unfamiliar words may have been difficult to pronounce. Also, the meaning may have been difficult to understand as well. This example is similar to sight-reading music. Better your background knowledge (memory of notes and note patterns) the easier it will be to sight-read because you are using a larger memory bank to decode new patterns of information.