Recommended tire pressure is printed on the side of each tire. On Catrikes with Schwalbe Marathon Racer tires - the Expedition for example - the pressure recommended is 55 to 85 psi (pounds per square inch).

Incidentally, the amazing 2013 Catrike 700, has rear tire pressure of 145 psi and front tire pressures of 160 psi!!! If you put that much pressure into a tire recommended for lower pressures - such as those on the Expedition - the blast as it blows out will be heard like a gunshot! Don't overinflate!

Why such high pressure tires on the new 700? One ride will show you!
It reduces rolling resistance and allows the trike to accelerate very quickly and easily. It also prevents tires from 'rolling under' when cornering at high speeds. And, of course, it prevents "pinch punctures" because the narrow tires are so hard that they virtually don't compress when hitting rocks or bumps.
Gives a firm ride, yes, but you're sitting on a "chaise lounge" seat and the extra performance is definitely worth it to some people!

For best performance go with the higher recommended figure on the side of your particular tire.
The only time I don't inflate to the highest recommendation is if the bike will be sitting in a closed car at the height of summer - when extremely high temperatures will cause air in the tire to increase in pressure and it may blow out the tire. Even then, I never knowingly go below the lower pressure recommended on the sidewall.

There are two main types of valves used in bicycles. Schrader valves are the same size as those used in automobiles and some bicycles, mountain bikes in particular. They can be inflated by the air pump at most garages or service stations.

Your Catrike & many other high end bicycles have a thinner type of valve called a PRESTA VALVE.

When you unscrew the valve cap from a Presta valve, you find a small knob on top of the valve. It must be unscrewed to inflate, then rescrewed after inflation before putting the valve cap back on.
Most bicycle pumps come with two holes at the end of the hose... one for larger Schrader valves. The second, smaller one is for Presta valves.

It is common to have an air pressure gauge on the bigger hand pumps so you know exactly what the pressure is while inflating the tube/tire. Most small pumps carried for emergency use on bikes do not have a gauge, but some slightly more expensive ones do.
If you purchase an adapter - about $3 at bike shops - you can use the regular service station pumps to inflate your presta valved Catrikes or bicycles.

One final point, check your tire pressures regularly! Even when in storage, tires lose small amounts of pressure over time. It definitely pays in performance and reliability to keep tires properly inflated! You can purchase a small air pump with a pressure gauge at your bike shop.