How do I vent shingle roof with no attic with valley thats gets ice dams?

Venting and ice dams are mostly unrelated issues. Ice dams form because the eaves on your roof are over less-heated (outside) space and get colder than the rest of the roof. In freezing temps, the warmer upper roof will melt snow or ice which runs down and then freezes at the eaves. More water runs down and freezes, forming the ice dam and then the ice dam starts pushing back up the roof and under the shingles. The solution for the ice dams is exactly what RMDman said, Ice & Water shield.

After the roofers tear off the shingles and clean up the roof deck, you are required by building code to put down enough ice and water shield to extends 24" inside the outer wall. For most roofs in Zone 5, that means two overlapping layers (about 5 1/2'). See Ice-Dam Protection: How Far Up the Roof Slope?. Doing the entire roof is extremely cheap leak prevention insurance and I second the recommendation.

Do I need to vent this?

Conventional wisdom and most roofers will say yes. There are alternatives. Do a search on "unvented roof assemblies" and pay careful attention to the articles on the Building Science and Fine Homebuilding sites. Once you understand the science and the rules (dew points, condensing surfaces, drying potential, etc.), it gets easy to understand the building code requirements.

It may be less easy to convince your builder / roofer. If you spec an unvented roof assembly, your builder may say things like, "I won't warrant this" because he/she has no experience doing it and is worried about a callback that'll cause him to lose money on your job. I ran into such issues when I did my roofs so I did them myself.

Unvented assembles tend to cost a little more, but I very much recommend them because you can get more insulation in the available space. More insulation is typically the household expense with the fastest cost recovery.

How do I vent shingle roof with no attic with valley thats gets ice dams?

Venting and ice dams are mostly unrelated issues. Ice dams form because the eaves on your roof are over less-heated (outside) space and get colder than the rest of the roof. In freezing temps, the warmer upper roof will melt snow or ice which runs down and then freezes at the eaves. More water runs down and freezes, forming the ice dam and then the ice dam starts pushing back up the roof and under the shingles. The antidote for water coming through the roof from ice dams is what RMDman said, Ice & Water shield.

After the roofers tear off the shingles and clean up the roof deck, you are required by building code to put down enough ice and water shield to extends 24" inside the outer wall. For most roofs in Zone 5, that means two overlapping layers (about 5 1/2'). See Ice-Dam Protection: How Far Up the Roof Slope?. Doing the entire roof is extremely cheap leak prevention insurance and I second the recommendation.

Do I need to vent this?

Conventional wisdom and most roofers will say yes. There are alternatives. Do a search on "unvented roof assemblies" and pay careful attention to the articles on the Building Science and Fine Homebuilding sites. Once you understand the science and the rules (dew points, condensing surfaces, drying potential, etc.), it gets easy to understand the building code requirements.

It may be less easy to convince your builder / roofer. If you spec an unvented roof assembly, your builder may say things like, "I won't warrant this" because he/she has no experience doing it and is worried about a callback that'll cause him to lose money on your job. I ran into such issues when I did my roofs so I did them myself.

Unvented assembles tend to cost a little more, but I very much recommend them because you can get more insulation in the available space. More insulation is typically the household expense with the fastest cost recovery. More insulation will reduce heat loss through the roof assembly. Less heat loss means less melting on days when the temps are below freezing, and less melting on those days means less damming.