If you haven't already, please read my TIPS page that explains some terminology and pieces of equipment.
OK, so lets assume that you have a compact camera or even an iPhone - how do you take good photos?
First, you need to hold the camera correctly. I have seen so many people holding their camera at arms length and squinting into the lcd screen with their arms moving about all over the place. To take a sharp photo, you need to hold the camera steady. If possible find a place that you can rest your camera on or against like a wall or a post. Failing that, keep your elbows tight against the sides of your body to help remove the movement in your arms. If your camera has a viewfinder as well as a lcd screen then use it. Holding the viewfinder to your eye while holding your elbows to your sides will form a three point contact which is reasonably stable. You can also get small flexible tripods called "GORILLAPODS" which can be used like a normal tripod or can be wrapped around any convenient pipe, post or fence.
Now look at the composition in the screen or viewfinder. Are there any unwanted distractions in the photo like a pole sticking out of your partner's head or a parked car or a trash can? If so move around until the composition is better. Most compositions follow the rule of thirds - image your photo divided into 9 rectangles (3 rows & 3 columns). The main subject is usually best placed at any corner of the centre rectangle. This isn't a hard and fast rule, it can be broken, but it will usually provide a more pleasing composition. Subjects moving from left to right or away from you are best placed on the left side to give them space to move into, while subjects moving right to left or towards you are best placed on the right. For landscapes generally place the horizon along the top edge of the central rectangles. If the sky is more interesting than the foreground, place the horizon along the lower edge of the central rectangles. Placing the horizon along the centre of a photo generally produces a dull, static image.
When pressing the shutter button, don't stab at the button as this will move the camera. Initially, press the button slowly about halfway to engage the autofocus. This is usually confirmed by a green focus rectangle appearing on the lcd screen. Next simply press the button all the way down using a rolling motion of your finger to give a smooth action.
Have a look at your photo. If it doesn't look right try to figure out what is wrong. If it is blurred did you move or did the subject move? If the composition looks wrong try to determine what you can do to improve it. Then try again. I take hundreds of photos on a day out and I only maybe publish 20 - 50, so don't be discouraged - just keep trying.
GOOD LUCK !