Preparing the vector.

1. Cut 1 to 5 ug of vector with the desired restriction enzymes.  You'll only require 50 to 100 ng to clone a fragment, but the excess provides opportunity for checking the completeness of the digestions and for being certain that you have enough at the end of all the manipulations. Check the completeness of digestions by comparing 20 ng of uncut vector to 20 ng of cut vector on a minigel.  It is critical to get as complete digestion as possible because the uncut vector generates a background of transformants.  If necessay, you might consider gel purifying the cut vector, but I wouldn't recommend this as a solution if the vector is not cutting well in the first place.
If you need to cut the vector with more than one enzyme and the cut sites are close together (like in a polylinker), it is very difficult to know whether both enzymes have cut.  I recommend cutting half the the DNA with one enzyme and the other half with the other enzyme.  Check a small amount on a gel.  If both digestions are complete, then treat each portion of DNA with the enzyme that was missing during the first digestion.  There is no need to check the DNA after the second digestion because you won't be able to see the effect of the second cut.  Combine the two preparations of DNA and proceed to the next step.
2. Once the digestion is complete, heat inactivate the restriction enzymes if possible (check NEB catalog) or phenol extract followed by chloroform extract.
3. Ethanol precipitate the cut vector.
4. Dissolve the DNA in 20 ul of 1X SAP buffer (shrimp alkaline phosphatase buffer), which can be found in box Y in the freezer.
5. Add 0.2 ul of shrimp alkaline phosphatase (SAP) and incubate for 1 hour at 37^oC.  SAP removes 5' phosphates from the vector so the vector can't ligate on itself.  I recommend SAP treating the vector even when the vector has been cut with two different enzymes, which would render the ends incompatible, because there is often some singly cut vector in the preparation.
6. Heat inactivate the SAP at 65^oC for 20 minutes.
7. Determine the DNA concentration and store the SAP-treated vector in the freezer.  Make certain to indicate on the tube that it has been SAP-treated.

PCR amplifying the insert.

Setting up a typical PCR reaction with Pfu polymerase:
Assemble all components on ice to reduce the chances of nonspecific priming.

H2O	template DNA	5 ul of 10X Pfu buffer	1 ul of 10 mM dNTP	20 pmoles of one primer	20 pmoles of the other primer	1 ul of Pfu polymerase	PCR conditions.
Calculate so final reaction volume is 50 ul	picograms of target should be sufficient, but I typically use nanogram amounts	This is supplied by the manufacturer.	Each of the deoxynucleotides is present at 10 mM	Primer stocks are typically at 100 pmoles/ul		Add this last and keep the reaction mix on ice to minimize mispriming.	Preheat the block to 94 degrees before inserting the reaction tube to minimize mispriming.  Then follow the guidelines provided below the table.

1. Denature the sample at 94^oC for 3 minute.
2. Calculate the Tm for the region of each primer that matches the target and allow the primers to anneal to the template for 1 minute at a temperature that is 5 degrees below the calculated Tm.
3. Extend for 1 minute at 72^oC.
4. Denature the sample at 94^oC for 1 minute.
5. Anneal the primers for 1 minute at the same temperature as given in step 2.
6. Extend for 1 minute at 72^oC.
7. Denature the sample at 94^oC for 1 minute.
8. Calculate the Tm for the entire length of the primer.  If it is greater than 70^oC, use an annealling temperature of 65^oC.  For a Tm less than 70^oC, use an annealling temperature that is 5^oC below the calculated Tm.  Allow the annealling to occur for 1 minute.
9. Extend for 1 minute at 72^oC.
10. Repeat steps seven to nine 28 more times.
11. As the final step, allow an extension time at 72^oC for 10 minutes and then hold the sample at 10^oC until you have a chance to place the sample on ice or in the freezer.

Isolating the PCR insert (this skips gel purification and assumes that the desired fragment is the major product in the PCR reaction).

1. Add 150 ul of 0.1 M NaCl, 10 mM Tris pH 8, 10 mM EDTA to the PCR reaction.
2. Phenol extract the diluted PCR reaction 2 times.  For each extraction, the volume of organic solution is approximately equal to the volume of aqueous material.  If the interface between phases is clear, remove the organic phase with a pipette and discard it.  If the interface is cloudy, transfer the aqueous phase to a fresh tube.
3. Extract 1 time with Ether and then incubate at 37^oC for 5' to evaporate residual ether. (In this case, ether is used instead of chloroform to remove the residual phenol because any chloroform left at the bottom of the tube could interfere with the subsequent spermine precipitation.
4. Add 10 ul of 100 mM spermine. Perform steps 4 through 11 as described in the spermine precipitation protocol.  This involves spermine precipitation followed by ethanol precipitation.  Use Sodium Acetate when you dissolve the spermine precipitate.
I recommend using spermine precipitation because it removes primer and nucleotides leftover from the PCR reaction.  I'll note that the same can be achieved by gel-purifiying the PCR products.  Spermine is reported not to precipitate fragments less than 50 nucleotides.  I'll also note that I've successfully cloned PCR fragments that have not been spermine precipitated; these were only subjected to organic extractions and ethanol precipitation.
5. Dissolve the ethanol precipitate in TE (typically 20 ul) and check the concentration with the fluorometer.
6. Digest the DNA with the desired enzymes.  Cut several hundred nanograms if possible, which should be more than what is needed for a typical cloning.
7. Inactivate the restriction enzymes with heat or by phenol extraction.  Check the New England Biolabs catalog for a list of enzymes that are susceptable to heat inactivation.
8. Store the fragments in the freezer.

Ligating the fragments.

1. Set up ligations between the PCR product and vector fragment.  If necessary, ethanol precipitate fragments so the ligation reactions can be set up with appropriate amounts of DNA.  I recommend using 100 ng of vector (3 to 15 kb) and 6 fold molar excess of insert when ligating the insert into a single vector fragment.  Although the ligase preparations come with 10X buffer, I usually put the fragments in a total volume of 20 ul of NEB buffer 2 supplemented with final concentrations of 1 mM ATP and 100 ng/ul BSA.
The Maniatis cloning manual  (see page 1.68) recommends that you heat your DNA at 45^oC for 5' minutes before adding buffer components or ligase to the reaction.  This heating step melts ends that have annealled together.  I rarely do this, but you might try this if you aren't getting enough transformants.
2. Ligate overnight at 15 ^oC.
I strongly recommend comparing a portion of the ligated material to non-ligated material on a gel.  In addition to ligating to the vector, the PCR insert should ligate to itself and form a ladder.  If you don't see this ladder, it would suggest that the enzymes failed to cut the ends of the PCR fragments.  In this case, the ends of the fragments are not phosphorylated so the PCR fragments will be unable to ligate to each other or to the vector (unless the vector has a blunt end).
3. Store the DNA in the freezer until you are ready to transform bacteria.

Transforming E. coli.

1. Use the transformation procedure described here.  I usually use 6 ul of the ligation mix.  Unless you are certain that the cells are good,  set up a no DNA control and a positive control with 1 to 10 ng of uncut vector.
2. A description of Blue/White screen, which you might employ with pUC or BlueScript vectors is provided here on the latter half of the page.  This link also provides a description of how to prepare LB plates.