Follow the code snippets in the Concepts page:
ProConcepts Geoprocessing · Esri/arcgis-pro-sdk Wiki · GitHub
The code snippet for opening a tool dialog is (available in the above link):
string input_points = @"C:\data\ca_ozone.gdb\ozone_points";
string output_polys = @"C:\data\ca_ozone.gdb\ozone_buff";
string buffer_dist = "";
var param_values = Geoprocessing.MakeValueArray(input_points, output_polys, buffer_dist);
Geoprocessing.OpenToolDialog("analysis.Buffer", param_values);
As the execution runs Asynchronously, you need to use "await" keyword:
// get the model tool's parameter syntax from the model's help
string input_roads = @"C:\data\Input.gdb\PlanA_Roads";
string buff_dist_field = "Distance"; // use the distance values from a field named Distance
string input_vegetation = @"C:\data\Input.gdb\vegtype";
string output_data = @"C:\data\Output.gdb\ClippedFC2";
string tool_path = @"C:\data\CompletedModels.tbx\ExtractVegetationforProposedRoads";
var args = Geoprocessing.MakeValueArray(input_roads, buff_dist_field, input_vegetation, output_data);
var result = await Geoprocessing.ExecuteToolAsync(tool_path, args);