I think that the best way to start improvising is to consider the way you think about a simple melodic line, as when you compose.
What do you do when you want to start composing anything?
I think, you'd start from a melody, that could be a series of ritmic figures,
or just an arpeggio from the tonic to the dominant or anything else,
but u start first from the melody and then you get from there the armonies.
So, i think you should just take your instrument, think of a key you like a lot.
I like F major, it reminds me the gold yellow of the sun, those great days full of light, warm, summer, or my time with my friends or family...
Something i really feel dear to me, my city...think of that, and then start with something.
Give you some parameters, like i will start my F maj in with A, C, F...then i keep pressed F
and then i go with a little scale to C and then whatever it comes, but
LET YOUR HEART SPEAK you will feel better.
Think that music is nothing but another language in which, there are words that make sentences,
there are meanings to those words and there are affermative, negative or interrogative sentences,
and you also have periods, and grammar to link all that.
So just think that you want to give somebody, even yourself, a sense...and you must think first about yourself..
since if it has non sense for you, then will be hard that it is understandable for anybody else.
Once you have got that, then just let it go.
One day it will be not that great, the day after you'll see a little improvement,
and as long as you keep trying...as when you train yourself with anything, you will see your improvements.
I also suggest you to record yourself, so you can pratically see where you make mistakes and on what you have to work on...
But, there's no written rule for improvisation, there's not a tecnique; you can't write rules for improvisation, since there are many different styles,
many different things that go on with that, just because all is linked to what your heart tells you. If you like pop, you'll find it into listening
to that music and getting that "vocabulary" but as with any language, once you have the words, and you know the meaning of them,
you can start automatically "talking" in music, as you do when you are a child.
Before being able to read, you can talk, you know the words and you know their meanings...
why??
Because your parents talk to you, the TV and the Radio tells you words, so you listen and you start talking...
same thing with music, you listen to classical music, you start thinking those melodies, those armonies, those expressions, those words...
and you begin working on them and making them yours, with your own way of "speaking", preferring some sentences, to others...
as you do with a language. so listen to a lot of music, take a score and read it while u listen to it, then do it again just in ur mind, then go play it and so on...
practice that way, then start some easy melodies on all the keys you like,
if you are a composer you know how to go with armonies and linking one key to another. go for that...
but DO IT...it will go automatically, nothing is wrong. all is good. somebody as something to say?? whatever.
Just express what are your inner thoughts.
this is the best advice i can give you, and i apologize if i made any non sense in it, english is not my language, so if anything or everything makes no sense,
i'll be super happy to try to work it in another way to make it more clear
Best wishes! and have fun!