For Fruit Syrup

1. Blend fruit with the lemon juice until smooth.
2. Strain it through a fine sieve/mesh strainer for a smooth syrup.
3. Combine the fruit purée and sugar in a small saucepan, and bring it just to a boil. Simmer until it thickens and coats the back of a wooden spoon. 
4. Cool completely, spoon into glasses and pour in club soda or sparkling mineral water.

For Basic Simple Syrup

1. Combine the sugar or honey in a small pot.
2. Bring the mixture just to a boil, then remove it from the heat.
3. If you're making a lemon/lime/grapefruit/orange/ginger syrup, add your flavorings and steep for 30 minutes to an hour. Strain out or remove the fresh flavorings and chill the syrup.
4. If using a concentrated extract such as vanilla or root beer, add 1-2 tablespoons depending on how strong a flavor you'd like. Taste and see is the best method.