This is intended only to give brief instructions. For details about why some of it is being done this way, check the internet.

Blanche

Blanche all vegetables before freezing. Boil 60-90 seconds, plunge into water bath to stop the cooking process.

Asparagus

Chop into 3 inch pieces. Blanch 3-5 minutes depending on thickness. Will keep for up to 18 months. Good for soups, etc., but will not be crisp for a side.

Avocado

Will keep for up to 18 months.

Broccoli

Cut into bite sized florets. Blance 3 minutes, then put into a large towel and toss to get as much water out as you can. Freeze the pieces whole in single-use zip lock bags. Good steamed or boiled (2 minutes) or in stir fries, quiches and soups. Broccoli will not have the crunch, but will taste OK. Use within a year.

Cabbage and Brussels Sprouts

Soak in heavily salted water for 30 minutes to encourage pests to vacate. Pick off any old leaves, and trim base off.

For cabbage: Quarter (leaving the stem intact) and freeze. Keeps only about six months.
For Brussels Sprouts: Blanche 3-5 minutes depending on the size. Move to freezer immediately on a rimmed cookie sheet. Freezing will actually improve the flavor, and they will keep about 18 months.

Cherry Tomatoes

Don’t require blanching. Rinse well, dry and freeze. Will keep for up to 18 months. No longer good for salads, but good for soups, stews, braises, roasting, etc.

Corn

Freeze within 10 hours of being picked, not corn from the supermarket. Remove kernels from the cob. Blanche for 4 minutes. Freeze on a pre-cooled tray so kernels stay separate. Good for stir fry or on your plate. Will keep for up to 18 months.

Cucumbers

These are best preserved by pickling. Read my collection here.

Garlic

This can be dangerous. READ CAREFULLY. You can freeze peeled garlic in ice cube trays in olive oil, but DO NOT keep at room temperature for more than a few minutes. EVER. Botulism develops quickly. Go straight into the freezer, and then straight from the freezer to the pot or skillet and cook immediately. The bacterium Clostridium botulinum can cause death in a few days without medical treatment. It is safe only if you do it perfectly right.

Green Beans

Blanche, then freeze individual beans laid flat on a pre-cooled tray. Good for stir fry and soups. Will keep up to 18 months.

Green onions

Freeze greens and whites separately. The greens freeze well without any processing. Blanch the whites for three minutes, and then freeze. Double bag to avoid onion smell in your freezer. Will keep for up to 6 months.

Mushrooms

Do not blanche! Wipe them clean with a dry towel and cut off the end of the stem. Freeze individually on a tray overnight, then seal in a vacuum bag. Use within a year as you would fresh mushrooms.

Pumpkin, winter squash, acorn squash, etc

Bake at 350°F for 45 minute, scrape out flesh and let cool and then puree. Freeze flat in zip lock bags.

Spinach

Will keep for up to 18 months.

Tomatoes

Blanche whole, then remove skin, cut into pieces, then freeze in zip lock bags that lay flat. Not good for salads, but good for sauces, soups, etc. Will keep for up to 18 months.

Zucchini

Good for bread, saute, grilling, muffins, pancakes, lasagna, frittata, pizza, quiche, and more … Cut into pieces and blanche 3 minutes. Pat dry and freeze in single-use zip lock bags.

Will keep for up to 18 months.

Don’t freeze:

Eggplant: You can, but it will be for babaganoush, etc. Otherwise use only fresh eggplant and freeze before seeds mature; even then freeze Black, but not Chinese or Thai.
Celery: This is mostly water and doesn’t freeze well, and it is readily available in the grocery. Otherwise, blanche 3 minutes and freeze in sticks.
Onions: Cut into large pieces and blanche 5 minutes. Freeze in a layer and break off what you need for stews and soups. They will be mushy, but retain flavor.
Lettuce: Not good for anything other than flavoring stocks and soups.
Spinach: Not good for anything other than flavoring stocks and soups.

Rather than reinventing the wheel, the following text is from MyBluePrint.com.

From MyBluePrint.com

How to freeze vegetables

Here’s your comprehensive guide to freezing all kinds of vegetables.

Avocado

Storing in halves:

Cut the avocado in half; remove the peel and the seed.
Rub the exposed fruit with lemon juice.
Putt into an airtight container or freezer bag. (No need to pre-freeze.)

Storing as purée:

Purée the avocado.
Mix in a few drops of lemon or lime juice to prevent browning.
Transfer to an airtight container.
Freeze for up to 3 months.

Blackberries

Wash and pat dry.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 6 months.

Note: Berries can really benefit, texture-wise, from adding a little sugar before freezing. If desired, toss the berries with sugar (about 1/3 cup per pint) before pre-freezing.

Blueberries

Wash and pat dry.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 6 months.

Cherries

Wash your cherries.
Remove the stems and pits.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 6 months.

Cucumbers

Slice the cucumbers and remove the skin if desired.
Pre-freeze.
Transfer slices to an airtight container.
Freeze for up to 3 months.

Note: A cucumber will absolutely lose its texture when frozen — it won’t have any crunch. Instead, consider making freezer pickles, which are said to retain crunch (here’s a recipe).

Eggplant

There are actually a few different methods of freezing eggplant. Here are two:

Method 1:

Blanch the eggplant for 3-4 minutes, then plunge it in ice water to cool.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 3 months.

Method 2:

Slice into coins, and bake at 350 F until tender, 10-15 minutes (not totally browned).
Remove from oven, and let cool.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 3 months.

Tomatoes

Blanch the tomatoes for 1-2 minutes, then plunge in an ice water bath.
Let dry, and cut into chunks or pieces if desired.
Pre-freeze.
Transfer to an airtight container.
Freeze for up to 6 months.