See a doctor.
I've had similar. Had to see a urologist and had a few tests, first test was measuring my output and input by measuring all drinks and recording them, and measuring all wees and recording them, for three days. Second test was a urine flow test in which I had to pee onto a machine, which recorded the force/length/amount of urine plus any stop/starts or dribbling after weeing; after that I was given an ultrasound to check how much urine I hadn't passed (Post Residual Volume rate) .. Due to the results of the tests I was then given a cystoscopy and urethral dilation, and have since had to be catheterised as well.
Of course, your's could be as simple as a UTI and so it's good to see a doctor pronto really to get it checked and treated..
The basic advice from the doctors is that when you wee, everything needs to come out really. What stays can eventually build up over time and lead to serious problems, or it can cause a loss of bladder tone/elasticity, or infections. So you need to be getting this sorted. There is a safe level of urine that can be held onto, but even this isn't ideal or very normal! In the meantime, relaxation whilst on the loo is most important, though, if you can take a book or even an iPod or something in, so that you remain standing/sitting until you feel you've completely emptied, might help. Like for example giving yourself twenty minutes of interrupted time with no worrying/straining etc. FWIW straining will in the long run only make things worse anyway, apparently it causes hypertrophy of the muscles if done over a long time..