Northern Virginians go to the polls Tuesday to elect a new governor, lieutenant governor and attorney general as well as 21 members of the Virginia House of Delegates. Voters in Northern Virginia -- Arlington, Fairfax, Loudoun and Prince William counties and Alexandria, Falls Church, Fairfax City, Manassas and Manassas Park -- also will find a number of local races on the ballot. In Fairfax and Arlington, there will be several bond issues for projects ranging from jail expansions to school construction.

Polls in all jurisdictions will be open from 6 a.m. to 7 p.m. Party designations are not included on Virginia ballots; write-in candidates are permitted in all races.

The election this year has been dominated by the governor's race -- a fierce struggle between Lt. Gov. Charles S. Robb of McLean, the Democratic candidate, and Attorney General J. Marshall Coleman of Staunton, the Republican candidate. With few major issues separating them, Robb and Coleman have turned to harsh personal attacks, fighting a bitter radio and television duel that has helped produce the most expensive governor's campaign in state history.

Only two states are holding gubernatorial elections this year, and some national Republican leaders consider the Virginia race to be a referendum on the Reagan administration, with Coleman tugging hard on the president's coattails.

Throughout the campaign, the Coleman camp has attempted to portray Robb, son-in-law of Lyndon B. Johnson, as an outsider who married his way into the Virginia political spotlight. In a campaign where both candidates have stressed their conservative politics, Coleman has attempted to link Robb with the liberal Johnson philosophy, labeling him a "son of the Great Society."

Robb, who has been running ahead of Coleman in recent voter polls, has fired back sharply. Early this fall, the Robb campaign took to the airwaves to charge that Coleman was soft on enforcing drug laws, and last week charged that the Coleman campaign was enmeshed in conflicts of interest.

By election day, Coleman estimates he will spend $2.9 million on his campaign and Robb estimates he will spend about $2.5 million. Hefty radio and television advertising bills account for much of the costs in the race for a job that pays $60,000 a year.

The governor's campaign hasn't been the only race to produce political sparks.

In the campaign for lieutenant governor, GOP candidate Nathan H. Miller, an attorney and a state senator from Harrisonburg, has been dogged by charges that he promoted legislation that could have benefited his legal clients. Although Robb has urged the Senate Rules Committee to delay its investigation of the conflict-of-interest charges, both Robb and his running-mate, former Portsmouth mayor Richard J. Davis have hammered at the allegations.

Miller claims the legislation has presented no conflict and has accused his opposition of manufacturing bogus issues.

By contrast, the race for attorney general has produced relatively few points of contention and little controversy, with both candidates -- Republican Wyatt Durrette Jr. and Democrat Gerald Baliles -- finding few areas of disagreement. Durette is an attorney and a former legislator from Fairfax County and Baliles is a Richmond attorney who has served in the House of Delegates since 1976.

The other major elections this year are for the 100-member House of Delegates. Most campaigns in Northern Virginia got off to a sluggish start, hampered by uncertainty over the new redistricting plan.

Following a special session of the Virginia General Assembly, the legislators produced a plan that immediately brought sharp criticism from throughout the state and nine lawsuits contending the plan was both discrimatory to blacks and unconstitutional.

This summer, a special judicial panel ruled that the plan is unconstitutional, but allowed the elections to proceed.

Under that ruling, the delegates elected Tuesday may serve one-year terms, instead of two. The General Assembly must draw up a new redistricting plan by Feb. 1.

Republicans are optimistic they will continue to make gains in the Democratic-dominated House, especially in Northern Virginia. Democratic strength in urban areas such as Arlington and Alexandria has been eroded by the population declines of the past 10 years. Meanwhile, Republicans have gained power in the traditionally conservative, growing suburban districts of Fairfax County, Loudoun and Prince William counties.

In Northern Virginia, there are elections in eight House districts -- one each in Alexandria, Arlington, Loudoun and Prince William counties and four in Fairfax County. Few substantive issues have surfaced. Most candidates have complained that their biggest headache has been trying to get the attention of voters, confused and uninterested because of the redistricting controversy.