I would suggest removing and dis assembling the carb, thoroughly clean and rekit it, install new fuel lines. If you've never done this before, we can point you to carb service manuals containing detailed explanations on how to do it.
hth,

1) If ZAMA carb, download the Zama Technical Guide and Quick Kit Cross Reference here:

http://www.zamacarb.com/tips.html

2) If Walbro carb, identify model and download appropriate service manual here:

http://wem.walbro.com/distributors/servicemanuals/

and to find correct kit, enter model no., e.g., wt-324 in "Search by Walbro Part #" here:

http://wem.walbro.com/walbro/family.asp

To hook up fuel lines:
1) connect the top of carb hose to the short primer bulb stem.
2) The bottom carb hose to the fuel line that has the filter on it inside the tank.
3) Finally, connect the remaining fuel line that comes out of the fuel tank to the center or the longer stem of the primer bulb.

Thank you, does anything connect to the hose barb in the tank?

The tank has two lines, 1 with the fuel filter on it and, the other is just a return line from the air purge bulb. Some manufacturers will put a little plastic coupler on end of return line in the tank to, ostensibly, keep it from pulling out, nothing connected to it on the inside of the tank.