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While all the other points are really good, in my opinion this is the most important thing to consider when making transitions. I would personally stretch the point even further and say: "Why transition at all?" I think that there's a merit to having a transition between two (or more) songs if there's a justifiable reason to have multiple source material in the first place. And I'd assume that if there is a good reason to have multiple source materials, then it'll probably be because of a good link between the songs which makes the question kind of obsolete. I think that rather than searching for a "transition" it makes more sense to look for a "cohesion". Of course there are some scenarios where you might be assigned to, or could even get paid to combine "contextually preferably uncombinable" things, and in that case I would definitely read the points made above a few times and really think about them because they're all very expertly made and elaborated on. This summer I got a job to write a big band arrangement for someone and she had some very specific form structure in mind that I personally would never use. But since I got paid to do the job, and she didn't really listen to my suggestions to change it to something more effective I just had to roll with it. It happens, and in such cases it's good to be able to do it. But these situations are outside of the point that I'm trying to make at the moment. To be honest, when remixing I think it's better to ask yourself: "How do I get more out of my source material so that I don't need to transition to a different song halfway". And when you really want to add another source tune, think to yourself: "What does this add to the music?: "How is this related to the rest?" "Where do I want to go?" "What do I want to say?" And when you're able to answer those questions with justifiable reasons, then the proper way to transition between songs will naturally come out of that. It's a very context specific thing, and the answer can be many things. In my experience, shifting too many times in one song between different genre's, source material, writing styles and all that good stuff takes away more than that it adds, and it's often a better idea to just write multiple tunes. It might not be the answer you're looking for, but i did want to add my two cents, since I feel that many remixers and writers often overlook these kind of things and tend to jump into quantity rather than quality. Not saying that that's necessarily what you're doing since, as many have already pointed out, you didn't give any examples of your music, but it's something to always keep in mind when writing. And asking some of the questions in the previous alinea might also solve other problems you could be dealing with, such as problems with flow, dynamics, instrumentation, motivic development, style, diversity and musical coherence among many things.

A few basic tips: Listen to songs that carry out the style you are looking for, and try to make sense of what the structure is. You can even put it into your DAW to try to tempo-match, and then break it down into how many bars until each section is over. Where's the intro? Where's the outtro? Bridge? How are the dynamics changing over the course of the track? Common transitions make use of cymbals and other transition sounds, or perhaps drum fills, but good transitions tend to connect both texture and contour (especially when writing orchestral, which has "only" organic instruments). Not just the density of the elements present, but also, the elements should feel like they're working together. Make yourself write a melodic transition sometime, and with time you'll hopefully develop that (voice-leading) as simply a core skill. You can do a simple melodic transition by writing a melody that sustains through into the next section, but later on, you could improve it by making all the little elements around the lead work together to lead up to that new section. For an example, I tend to share this, since it's what I consider my personal best arrangement. Maybe it'll help. Have your friends listen to what you have and give you advice... including us. That means post a WIP, not just "help me".

Take elements of the things you are transitioning to and from and mix them together. If you're transitioning from something that is slow and legato to something that is a little faster and more detached, start altering some of the things near the end of the slow section to be more detached, so that the style change doesn't seem to come out of nowhere. Take themes from the later sections and introduce them as secondary themes in the current section. Essentially, it's just a matter of introducing stuff in little bits before you get there so that it doesn't seem like you suddenly arrived out of nowhere.

Hard to say what to improve without a WIP to listen to. Having just done a 13 minute, 7 track orchestral remix myself, all I can recommend is to place your songs in an order that help you (e.g. putting songs in the same time signature together, be smart about preventing massive tempo jumps, etc.) and take the time in the arrangement to ease the listener into the various sections. The latter can sometimes be achieved by dropping out elements of track 1 and slowly introducing elements of track 2 (e.g. hints of the melody) before fully transitioning into it, and sometimes you can go for a dramatic stop or fadeout and transition the listener into the new section with a drum fill or a transitionary element like a held string note or the like. Again, hard to recommend anything if I can't hear anything. Anyway, your best bet is to carefully listen at other tracks and get some ideas on how others do it. Something like Sam Dillard's stuff might help, or if you really wanna go pro something like Final Symphony (a suite of Final Fantasy music performed by the London Symphony Orchestra) might do the trick.