You need to be sure you have enough air pressure in the tires. Check the pressure often, low pressure often causes flats and other problems.
Also check the rim strips or rim tape. The strips or tape protect the tube from the spokes and spoke holes in the rim. The best protection of this type is Velox rim tape. It is available in various widths to match the width of your rims.
When installing an innertube it is very important to not pinch or otherwise damage the tube. Be very careful to not allow any part of the tube to be pinched between any part of the tire bead and the wheel rim.