Obviously the key to blending with other musicians is listening; generally speaking, you must try to hear the entire orchestration in order to know how to fit your part into it. Specifically, there are many different things to listen for, including:
Always try to be aware of who is playing the lead part, keeping in mind that it may not be the first trumpet, or first anybody! The lead voice can move around to all the various parts, including bass trombone. Be aware of when you have a lead voice; even if it is only 3 moving notes while others hold a chord, those notes should be subtly emphasized. Also be aware of smaller ensembles within the ensemble; your part may be part of a trio or duet, and should be phrased accordingly.
Phrasing and section playing are dependent on the style of music being performed; 8th notes land in an entirely different place in Latin music than in Swing. Being familiar with the style of music allows a player to phrase correctly. Anytime a player attempts new music it is wise to become as familiar as possible, not only with the particular piece, but with the style and the genre in general. Section size and makeup also play a part; being the only trombone in a 3-horn band has different requirement than being one of four trombones in a big band. Phrasing is also affected by the wishes and preferences of people such as composers, conductors, arrangers, orchestrators, artists, and band leaders. As an example, if a musician is in a band backing a sultry ballad singer, he or she should know to play softly and smoothly, in a relaxed feel, not loud and ahead of the beat, attracting attention to himself. Similarly, brass players should not be timid in their approach to Wagner or Mahler music.
Pay close attention to all phrase markings on the page (dynamics, articulations, Tempo markings, etc.), but also be aware that some markings will be wrong, and others will be missing. It is still necessary to hear lead voices to confirm the information on the page. Also be aware that some arrangers or composers have different interpretations of what some marking mean - be as familiar as possible with the writer's intent. Any section player who feels that his part may be wrong, either the notes themselves or the markings, should by all means bring it up in rehearsal for correction.
It can be useful and fun to be able to read other people's parts - knowing the transpositions or tricks to read F Horn parts, or Eb or Bb parts. It is possible (and not uncommon an occurrence) to join a horn section that has no trombone parts if you are able to read other transpositions.
To summarize, Listen, Listen, Listen! Be as familiar as possible with the material and the players around you, but the key to good section playing is listening and bringing your musicality to your part. Remember that inner parts are just as important to a successful ensemble sound as lead or principal parts. It can be very satisfying to blend harmoniously with other musicians in creating a well-phrased tight-sounding ensemble performance.