Learn how time signatures work. It isn't enough to simply play the rhythms as they appear in the music. You must know where the accents of a particular time signature fall. The top number in the time signature provides you with the number of beats in the measure. The bottom number tells you what note value creates the beat. In common time signatures, the quarter note holds one beat. In some complex signatures, other note values hold one beat.
Purchase a book with rhythms in it to practice different time signatures and rhythms at the beginning of each practice session. You don't need to play the rhythms, just clap them.
Obtain a book with sight singing excerpts. Practice these excerpts daily to improve your ability to sight read new music. The book does not have to be written for your instrument. A standard sight singing book will fit most instruments ranges.
Mentally play the rhythm in your head before sight reading. It is very rare, where you don't get a few moments to look over a new piece before playing. Look specifically for any places that the time signature changes and make a mental note of any complex rhythms. Figure out how to play the complex rhythms before moving on to the easier, standard rhythms.
Keep a steady beat in your mind while playing the music. Subdivide if there are notes faster than the beat for the piece. To subdivide, simply find the fastest note and use that rhythm as the basic unit of time. For instance, if there are eighth notes in the piece, then mentally tick off two eighth notes to ensure that your quarter notes are played in time.
Avoid stopping to fix mistakes when you are sight-reading. You are not expected to be perfect when sight reading a new piece, but you are expected to play as if you were performing. To do this, do not apologize for mistakes, and keep the music moving forward.